There are really two forms of "cloak" - the cloak and the cape. (Ignoring things like hats and handkerchiefs which are really only things you carry in your off hand as a distraction.)
The cloak is a long garment, It should reach from your shoulders to about your knees. The cape is shorter, hip or thigh length.
The cloak and the cape are both enveloping. They slow the opponent's weapon down by weighting it and surrounding it, making it difficult to move. They are not solid, so can't block a thrust, instead they slow it and perhaps move it off line a little. They are large, they cover a large area, so can be hard to move around when spread out.
To be most effective, both cloak and cape need to have some weight to them, and with cape you must learn how your particular one moves, so you can keep it close or fan it out as you please. A heavy cloak or cape can be tiring to use, and slow to move, so you don't want too heavy. A line of light rope at the bottom hem can help a cape to fan out, and add a bit of weight to make it more usable as a stick or buckler.
It is used wrapped around the arm, wrapped so it hangs on the outside of the arm. To wrap it, hold the middle of the neck in your off hand, then sweep the length of it up and to your inside, and over the arm. Wrap a couple of times, to make sure it's secure. It should cover all of your forearm, but no more of the arm than that.
To defend a cut:
To defend a thrust:
Hold it by the middle of the neck, or a little to one side of the middle, which ever makes it easier for you to control the movement of the cape.
It can be used in several ways:
Like a soft stick
You can hold the cape so it hangs together like a roll, and use it like a soft stick. This can take practice to stop it fanning out, try not to twist your wrist as you move the cape. You want the cape to be as close and compact as possible.
Then you use it like a soft stick, to sweep the opponent's weapon away, aiming for the beginning of the last 3rd of the sword - far enough from the hilt to get leverage, close enough to it to make disengaging difficult.
Like a soft buckler
You can use a cape in a similar way to a cloak, using the weight of the cape to envelop and slow the sword either by catching the point, or by dropping the weight of the cape onto the blade. As for cloak, step aside from the thrust at the same time.
You can also drop the cape onto the opponent's sword, either as an answer to an attack, or as preparation for your own attack. You want to slow the sword and make it hard for them to counter you. It should be done as part of your advance, rather than before moving, speed is important.
Fanning and throwing
Don't keep your cape hand still, it makes a very large target.
You can twist your wrist and fan the cape out to distract your opponent and hide your sword's movement from them. You can flick it to do the same thing, to draw their eye and distract them. The human eye is caught by sudden movements, and the bigger the movement, the bigger the response. So a large sudden cape movement will draw attention.
Don't make the fan so big that you blind yourself, or that you envelop or slow your own sword! Except in one case - you can fan the cape onto your sword, fling the cape at your opponent using the sword for leverage, then follow it with a fast attack from high ward where your sword is after being used in such a way.
If you throw it, aim for your opponent's sword or face. Even if it doesn't get to their face, it can cause them to blink or jerk back. You must instantly take advantage though, you have just thrown away half your arsenal, don't stand about waiting to see what happens, but follow up instantly.