It's sort of a difficult concept to explain in words, so busting out your Saturn is highly recommended. However, I will do my best to explain some of the noted details.
The Air Brake does indeed bring NiGHTS to a stop. But, if you hold down a direction just as you do the Air Brake, NiGHTS will sort of swing around in that direction. When it comes to paralooping objects with the brake, it goes something like this: fly towards the objects which you wish to collect, let off of boost, then use the Air Brake while holding a direction almost opposite of the direction in which you were flying prior. It's something you certainly need to get a feel for, as are many of the aspects of NiGHTS. After you do the brake, keep flying in the direction you were headed in before. I recall still making somewhat of a loop motion on the analog stick as I did this technique, but I'm not near my Saturn right now to double-check this. Just to clarify, this entire thing is done with one Air Brake, and it all goes pretty fast. That's the benefit! Good luck, and let me know how it goes for you.
~blackrabite