How to actually start cross play?

You don't. "cross play" just means that you can fight against people that own the ps3 version if your on your vita and vice versa

i dont think it actually supports crossplay. I think you can do this however. if you have a second account (and by second i mean a family member's account because having multiple accounts is not allowed =D ) use that account on the ps3 and invite your vita to join the game. now both will be in same game. and from what ive heard the lag is minimal enough that the vita player can watch the tv screen and play instead of hurting their neck. i dont have a vita mind you so this is mostly speculation/hearsay

You can't. Best you can do is what NewVirtue said and use a different account on the PS3 to play. 'Cross Play' simply means you can play against people that own a PS3 with your Vita, or for the PS3 playing against people with a Vita.