I distilled each paragraph into simple modern English, concentrating on the highlights of "Do this".
(mind you - Swetnam seems to have missed the concept of "sentence" never mind paragraph! So don't expect a one-to-one correspondence! The guy must have bought semicolons wholesale.)
It's available in several places, such as
Scans from the original text are by kind permission of The Academy of the Sword
Remarks in  are my commentary and explanations. I have tried to use swordside and daggerside rather than right and left, but those facing someone of a different handedness to their own will certainly have to experiment.
So here's the result, maybe it will help someone else!
Keep the rapier hand low, below waist level, and the arm straight. Hold the dagger in line with your dagger-side cheek, the arm straight and the point close to the sword point, two to three inches apart. Keep the points high, make sure you can see the opponent between them. Hold your head a bit to the swordside with your body forward. You should have your shoulders square on. [but your feet one forward one back, see later]
Don't put the thumb of the rapier hand on the blade, but on the nail of the forefinger. And see under grip below
Your sword foot is forward, and the heel of it should be in line with the middle joint of the toe of the off foot.
[The pic shows the feet at an angle, seeminly more than 45 deg but not as much as 90. The big difference to most stances is that the rear foot seems to be to the swordside of the front foot, most stances have it to the off side. This takes a bit of getting used to if you have been doing dagger as per DiGrassi, but it's quite stable and effective and gives you good reach.]
Carry the sword with the edge up and down, you parry with the edge. [I find it easier to have it more of a 45deg angle, turning my hand to parry with the edge. Do parry with the edge though, it makes the quillions more effective.]
Get all of them right - weapon position, stance, distance. It's no good practicing one and getting the others wrong. Read the book and start right, if you have had your feet wide apart as most men do, you'll find it hard to change.
The best way to get a decent stance and movement is to practice with a friend. Get your back to a wall, your partner stands about 12 feet away. Set your daggerside heel to the wall, and your swordside heel to the daggerside big toe. Now do a cut or thrust by stepping forward with the swordside foot and hand together but be sure to keep the other foot hard against the wall. Use it like an anchor, and step back again to be same distance from your opponent as you started. The wall will stop your foot creeping as it does if you are in room without a stop for the foot.
When your opponent cuts at you, either with sword or rapier, then take the blow on your rapier. Get your dagger in there as well, if it's at head height. Two weapons makes a good head defence. If you just use your dagger, the cut might slip past the point. Defend with both weapons, then drop the point of the rapier towards the opponent's body and at the same time lifting yourself up. Step forward as you thrust so foot and hand move together. This is quick and you can go for your opponent before he can recover.
Your sword foot is forward, and as near to the other foot as you can.
Standing in the guard position, look for where your opponent is weak in his guard. The better your guard is, the more obvious the holes in his will be. When you are ready and you see a hole, you step forward with foot and hand moving together to attack it. But as soon as you have thrust, get back into guard as quickly as possible, remembering to use the rear foot as an anchor and placemarker for your distance.
When you move, each foot should be solidly grounded before you move the other one. If the ground is uneven you might fall otherwise.
Be especially careful that you don't get carried away with the fight.
when standing in guard, keep the thighs close together. The forward knee should bend backward rather than forward. The more you "hollow" your body, the more you can have your body far away, the less chance he has to hit you.
If you block with the dagger, then let the dagger point fall, but not the arm. Especially don't move the arm so that you can't get it back where it should be to defend against another quick attack.
Have the dagger well forward, as far forward as the rapier point, and don't bring it back when attacking. The straight stiff dagger arm is the best defence with a dagger.
These last two are the strongest, but you should try all three, and use the one that works best for you. But practice them all because they are all useful in a fight depending on the circumstances.
For example, with the thumb on the blade you can do an overhand thrust, or a cut with the wrist which you can't with the other two. But the Stoccata gives you a couple of inches of extra reach. Use the one that gives you the most benefit at the time.
If you are fighting someone better than you are, use the one you are best at, if with someone who isn't skilled, then if you have practiced them all you can use any of them.
You have your points high enough to see your enemy between them so if your enemy attacks either side of your head you can meet it with both weapons. Then drop the point of the rapier to his thigh, turning your knuckles inward, stepping forward at the same time. Hit or miss, get back into guard as fast as you can.
Even though it's good to keep it high, if he comes at you, drop the point and skewer him. Parry with the dagger and drop the point of the rapier quickly to thrust at whatever bit of him is furthest forward or is otherwise open.
The best fighter there is, if he is fighting someone with skill, can't say "I'll hit him here", no more than a gambler can be sure he'll win.
So you can't say beforehand where you will hit, you have to look at his guard and see the opening, if you know how to do them well yourself. If you don't know how to guard, you won't see the holes. [I think this means that if you don't know why you guard in a particular way and the parries you can do, then you can't work out how to defeat your opponent's.]
If the opponent gets within your distance, then go for him at that instant whether he moved his body or his weapon or both. Put your point out but not too far, it must be ready to defend you as well as to attack. If you attack fully in the instant of his attack, then you might be in deep trouble if it was a feint, so make the first attack a short one ready to pull back if you have to. If he "bears his points anie abroad" [I think this means if he misses, but it may mean if he opens in his attack] then you can get inside his points and get to his face or breast or if his feet or leg is forward, get those.
As I said, look under both weapons. If you look over them with an eye, you will get hit on the head before you know it. Know and remember that the English tend to cut, and they fight furiously, with anger, striking usually to the head. So if you are using rapier and dagger, then expect a cut as often as a thrust and always defend it with both weapons. If your rapier point is under your dagger, then you can't get it up in time to ward the cut, so must take it on the dagger only. Or on the head! If you take it on the dagger only, if the opponent's sword hits near the point it might skip and hit you, or you might be fooled by the short length of the dagger.
If you make any movement towards your opponent - attack or defend - then make sure your feet move straight. If you step a bit sideways, then you lose a bit of reach. If you practice on a wooden floor, look at the floorboards. Your right foot should always land on the same board your left foot is on. The left foot should stay anchored in place, to guide the right foot back home so you keep good distance. Your shoulders should be square on to the opponent as if you twist, you aren't as stable or as ready to attack.
When you fight, fight nimbly and with speed. If you want to get in and fight and get away - which is hard to do if your opponent knows his job - You must have skill and judgement especially in knowing where his point is. You must be fast, because as soon as you see an opening you must take it.
An attack on the pass can come so quickly that an unskilled fencer can't see it coming until too late, and these attacks are fast and hard and very dangerous. But they can be defended against.
[great flights of fancy about hawks deleted. He thinks this passage thing is serious business]
Note that you can't judge the depth of your thrust on the passage as you can normally, you can't say "I'll hit lightly" as you are moving, you'll likely hit quite hard, it's hard to judge distance well.
If you feint to his knee, then very quickly change to the dagger shoulder or his face. Again it should be quick enough so he can't get his dagger back to where it should be. He shouldn't be able to tell if the false thrust is false.
The only way to guard one of these faints is with the rapier, if the dagger has gone down to block the feint, the rapier is the backup. move it across the body as you do if you just have single rapier, and that way defend all of you down to the knee.
Feints are useful to a rapier and dagger fighter against a sword and buckler. The rapier man (careful not to aim at the buckler) feints at the bucklerman's face and then thrusts at the knee or thigh. Or else you feint at the knee, and thrust for shoulder or face, so he has to try and defend with his sword.
The best way to make a feint is to strike down by the outside of your opponent's rapier hand, but not fully, and then bring up the point and go for his off shoulder. You don't want to feint within reach of his dagger, because he can move that faster and might just touch your point, and if he does he'll knock you off your timing, you won't be able to complete the real thrust before he's back on his guard. So feint to somewhere the dagger can't reach.
[After lots of arguments I think that he says "outside of rapier hand", because he expects everything to be parried with the dagger, even something on the swordside of the sword. With this feint the idea seems to be to get the dagger over to the swordside, so the dagger shoulder is clear. Most people you will be fighting will parry with the sword though, so beware. If your opponent does sword parries then feint to the inside of the sword to draw the dagger.]
There are many more guards [stances] that can be used with rapier and dagger, but most of them take a fair bit more practice than this one, and yet they aren't really any better, so I call it the Master guard. But in a school situation, the more the better as long as you use discretion and judgement. I've described them in a different book. Some times and for some purposes one might be better than another - you might find one works well against some particular man but one guard used all the time will become threadbare. So learn as much as you can, work out which ones work best for you, and use that one when things get serious. No teacher can make all students perfect in one guard, one might be useless at one, and good at another.
Your breast and belly seem very open, so your opponent will aim there for his first assault. If he aims a thrust above the waist, then move your dagger across, still upright, and push him over to the right.
If he attacks above the waist, then defend with the dagger, step forward with your off foot, and hit him where you can.
If he goes low, defend with the rapier by pushing down.
You must defend and attack at the same time.
If both of you are in this stance, waiting to see who moves first, then draw him by making a short thrust then getting back into guard quickly. When he comes in, defend then step forward with the off foot and attack.
If he is in this stance and won't be drawn, then charge him. Go for his wrist, or a drop a cut to his face, breast or knee. Come in at an angle by turning your knuckles inward. [I think this means that as your rapier is across your body, roll the hand so the fingernails are now upwards and this will make your point circle and chop down at an angle.] When the point is where you want to hit, thrust home. This thrust comes in at an angle, and is harder to defend from this cross guard than a straight one is.
Keep the dagger point upright and as high as your cheek and your rapier hand as low and as far back as you can. Your feet should be wide apart - 3 feet at least.
Many teachers say this is the best guard, for several reasons. They say the head is well back and so the face is safe, but I say the belly and front leg are in danger, and not easily protected. To be hurt in the belly is dreadful! If you use my guard, your leg and belly are well back. The face is nearer to your opponent but your dagger is in the right place to defend it.
If you have your leg forward and your feet wide apart, then you'll tend to pick up your front leg if someone thrusts at it, and this means you can't attack at the same time you defend. So when you do riposte, he'll be back in his guard.
[This next bit seems to be another guard, not the Stokata]
Keep your thumb on the rapier blade and the hilt of your rapier as high as your cheek, bending your swordarm elbow. Your feet should be as close together as possible. Your dagger hilt should be waist height, with the point upright.
The rapier point should be inside the dagger, and they should be close together. You should be looking under your rapier. Your dagger arm should be straight, not bent at the elbow. [it seems that the rapier point has to be off to the dagger side a bit. The blade seems to be crossing behind the dagger point about a 3rd of the way along the rapier blade, with the tip of the rapier roughly in line with your opponent's shoulder. Seems very odd....]
To defend, use the dagger. Keeping the point upright, move the dagger across your body to push the opponent's sword away. Don't turn the dagger at all. The opponent's blade will pass under your sword arm. As you move the dagger, riposte by lifting the hilt of your sword, turning your knuckles down, and hitting him in the sword shoulder. As you do this, step forward with your right foot. Foot and hand should move together, and your guard and attack are the same motion.
If your opponent comes forward with a cut, then you can defend with both weapons.
If you are charging him, then protect your sword shoulder by holding your dagger across to your sword side, point upright.
This is good against a lefthander.
If you practice this guard a lot, then you'll find it very good for both attack and defence, especially if you watch and wait your chance.
This will leave your belly and breast wide open, saying "hit me!" . When he comes in with a thrust, lift up both your blades and throw his sword off to the your swordside.
Don't lift your rapier hand, as you might endanger your own face. As soon as you have his sword clear of your body (you can clear it with one, but two is better), then get your point back in line and get him with an overhand thrust, turning your knuckles upwards into his sword side shoulder. [lift the hand, turn it so the fingernails are mostly down, and the point will slide into his swordside shoulder at an angle across his body. If you move your swordhand right back across your body in bringing your point into line, then you turn the fingernails up and go for his daggerside instead.]
This guard is very quickly and easily learned, and will defend against any thrust [Well, any thrust above thigh level ]
If your opponent feints at your breast or face to make you lift up your weapons so he can come in underneath, then bring down the dagger as quickly as you can.
[Both these two guards mean you must be very quick on your feet as you have to protect your legs by moving them out of the way, not by parrying.]
[He says "stiffe at the armes end, and a foote at the left asunder" which confuses me... does he mean the dagger is held wide but not the sword?]
Prepare by getting your rapier down as low as you can, your body almost lying on the ground, bending your offside knee very low.
[He says get your swordhand low, but then later that you have the opponent's sword passing under your arm. It looks like this is a lopsided stance, with your daggerside lower than your swordside, hence the bent offside knee. Or just don't go as low as he says, but fool your opponent into making the thrust over your swordarm by making it look like that's the best place.]
Then when your opponent comes in with a thrust you strike it towards your sword side with your dagger, so it passes under your rapier arm [He says under, but how if your swordhand is as low as you can?], and at the same time lift your rapier arm suddenly above your head. Turn your knuckles upwards [fingernails down] and the point of your sword down, over his swordarm into his breast or shoulder, stepping forward with your offside leg.
You need to be very quick to make this work, and equally quick to get back into guard.
If you use this trick more than once, then he'll expect you coming in from high up, so do that a couple of times then come in low under his sword arm and get him in the belly.
If your elbow joint is bent, then you don't have enough power to defend against cut or thrust. The best defence is to have the dagger at the end of a straight arm.
When you are parrying a thrust, turn your wrist so the point goes down but keep your arm straight. That way you can keep defending, as your wrist movement will be as quick as his thrust. If you move your arm, he can thrust again more quickly than you can get your arm back to where it should be.
Pay attention to the orientation of your knuckles and hand so that you parry or thrust correctly.
[I always try and block with the true edge of sword or dagger, which does mean turning the hand. The hand orientation can make a big difference to the angle of a thrust too.]
Your swordhand should be at waist height or lower, with your arm a straight as you can. The point should be a bit towards your offside, and also towards your opponent. Keep your sword on the outside of your opponent's sword, but don't touch it.
You mist keep proper distance - 3 feet or so between your points, and 12 feet from your front foot to your opponent's front foot. [Yet another case of don't trust the illustrations...]
Be sure you don't let your hand drift out to your side, it should be straight down.
[The illustration shows a swordfoot forward stance, pretty much the same as for sword and dagger, but with the swordshoulder forward rather than square on.]
Standing in this guard, if your opponent thrusts at you, then move your sword hand across your body keeping your point in his face until you've cleared the sword. Then drop the point and thrust at his thigh or body whichever is open. [He says "and turn your knuckles inwards" but I'm not sure why. No contortion of my hand in this guard after I've parried across into 4th seems to have my knuckles anywhere but inwards...]
There are many guards for single rapier, the Short Sword one is good on occasion as I'll explain when I come to that weapon.
Another way is to have your left hand on the blade, so you can use the strength of thumb and forefinger of your left hand to parry the thrust. Turn your swordpoint up or down depending on which way he comes in, then quickly thrust at him. [I'm not sure why only thumb and forefinger, rather than the whole hand on the blade.]
Another is to "stand upon the Stocke" [I have no idea what this is, it may be related to the Stokata, but I'm not sure how. Maybe it just means being ready to thrust.] and be ready to block your opponent's attack, but have your off side shoulder a bit forward of your swordside, offering it as a target.
When he takes the bait, bring your offside foot back so you wheel your body and his sword goes past. At the same time, thrust with your sword. This movement is your defence, don't try and defend with your sword.
He'll bring his sword across to parry, and unless he's very quick he can't get it back in time.
If he doesn't fall for the feint, then do it again but this time make the offside shot your real one and you'll hit him.
The best defence against this slippe is not to cut at all! But if you must, then don't over-commit, as you want to get back into guard as quickly as you can. If you do cut, then don't do it too hard, as you can get into trouble if you do. Use lighter more controlled cuts, and do them quickly. But it's better not to cut at all, but always attack with thrusts.
You can do something similar if he comes in close to you. If he's close you can't draw your sword back to disengage your point and thrust, but you can turn your hand and hit him. If he defends it as I outline below, then bring the point up suddenly and take him in the face or swordside shoulder.
When he drops his point to his offside to come under your arm, then drop yours too, towards your offside, so you'll meet his point as it comes. When he brings his up, bring yours up too, back into your guard
He will have to try to parry your feints as long as they are within distance so they look real, and so will end up flustered and unguarded.
[A classic one-two-three! Although I doubt it's in one fencing time with a four foot sword or a backsword, but a strong and practiced swordsman may well manage it. Note that the feints have to look real, don't just poke about.]
[I think the idea is to cross swords at some point, like the illustration, then turn your hand somewhat. See "A close at backsword" further on, it has a better description.]
Straighten your sword arm, and have your point sloping a little towards your off shoulder. Don't contact your opponent's sword, there should be a good three feet between your points.
If he charges in at you, then you can contact his sword by moving it across your body with your sword. When you do this, keep your point and hilt together, in the same relationship and angle.
[I have read these few paragraphs about backsword over and I think that's what he's saying, but a bit about protecting the face may mean that he wants you to keep the point still while you move your hilt]
Once you have moved his sword enough so that he can't hit you, then immediately drop your point and turn your knuckles inward [Fingernails on top I think] and thrust home into your opponent's leg. Step forward with your swordside foot at the same time, so your foot and hand move together.
Be careful you parry corectly. If you parry a blow or a thrust and you don't keep the point level, even if you are standing as per the picture, then your hand and face are open. Carry the sword about a foot in from your swordside, with your arm straight and no bend in the elbow. Be sure though that you can look inside it with both eyes, and that the point is sloping towards your offside shoulder.
If you carry the sword upright, then your opponent has three ways to attack you, especially if you have it upright right in the middle of your body as some people say you should. Hold it like that and you might cop a sudden cut to the head, and your arms are open too.
If you take the guard I describe, then only your offside head and your legs are open. You defend your legs by moving them, and yor head by parrying with the sword across your body.
[I'm not sure why the offside head is open when the point is sloping to the offside, it would seem the swordside head is in more danger, especially as it is swordfoot and swordhand forward.]
Now although the guard is called "back-sworde" whether you are armed with a two edged sword or a rapier, you should use this guard.
If your opponent cuts at your swordside head, then turn your wrist so the knuckles are outward.
[I'm not sure why he'd try a swordside cut, a cut to your offside would seem more likely. If you are standing very much swordside forward, then you wouldn't have to move your hand much to block that. But you would be a sucker for a feint I suspect...]
The idea is to keep your opponent at the end of your reach, he can't come close to you because of that point in his face. You have to be very strong in the arm though, else he'll beat your sword away and then quickly come in with a second attack.
If he tries that, then pull your sword in so the beat attack misses. He'll probably go off line as he was expecting resistance, and so his sword will carry over too far. If he does, then you can do an overhand cut to his sworside head before he can recover.
As you do that, step in with your rear foot so you get in close, turn your knuckles in [fingernails up] so your sword is under his and you get his point up over your head.
Once it's out of the way you can catch his hilt or wrist with your left hand (but the hilt is the easiest to hold onto). Then you can trip him or cut or thrust.
You can do this with a rapier too, if you can catch the sword close to your own hilt. This is because your opponent will have to bring his sword across his body to parry your face thrust, and so you can deflect his point to where it won't do you any harm, but you have to get in close, and be quick.