How do you Level up in AVA

In each match you play you earn experience points and supply points. The experience points you get will accumulate and you will rank up your character. The starting ranks don't have classes so you go through them pretty quickly (you prob already knew that). After you get get out of those stages the levels are then divided by classes. There are approximately 5 stages of classes to go through for each level until you are able to reach the next.
There is no sure fire way to level extremely quickly in the game but I would recommend playing through full matches to get all the exp you can. Play the objective well and you also be awarded with more exp. It also doesn't hurt to win because you get more exp than the losing team. Losers = Less exp and Gloating from little kids screaming "OM3 CHU R SUCh A N00b, jU ArNt A5 1E37 As M3h" all round long. Best to ignore those guys and stick it to them good. You will be absorbed in the fun and your exp bar will just fill up.

Hope this helped a little, probably didn't.