All I can say about aerial combat is dodging; stated in the Advanced Tutorials, there are three ways to do an Air Ukemi: left or right on the Left Stick to air Ukemi sideways, or hold DOWN to Ukemi as you're dropping down.
As for offensive techniques, it depends on each character really. Who are you looking into?
~So much knowledge, so little time. Let's get going and play to our heart's content~
Truly, learning how to fight in the air is top-level play. You may not be able to execute fancy high AP combos while hitting your opponent in the air, but the important thing is to make sure you're getting more meter than they are. Even if it's at a very slow pace.
Yeah I just don't like radec's air combat though. I feel like moves are just to knock you back so he can start sniping •_• though I'm starting to beast it up in close combat with him. I started playing the hardest bot difficulty in practice mode. Though the CPU doesn't like to jump much so I can practice arial combat