Well, it is pretty much as the title says. What's the best way to avoid grabbing? It's really annoying and more often than not I get damaged/killed as a result. At least 90% of my grabs are unintended, either because I wanted to continue with a down, up, attack or because I just wanted to run somewhere and an enemy moved in the way. It's especially bad when one is surrounded by enemies (left, right, up, down, air).
(All this refers to Gal only as it's the only character I've played so far. Still haven't beaten the story mode, despite playing for 15 hours so far (1CC only, no continues).)

I posting pretty late, but maybe someone will have the same question in future.

You avoid grabbing by pressing jump button. Also special pretty often breaking grab. Everything is in Training mode, which really good showing basic of movements, and combos in games :)