Log into the Account you used on the PSP onto your Vita and Select Transaction Management in [Account Management]. Select Downloads List and you should be able to download the games you've purchased on your account.
You can also look for the Games on the PlayStation Store.. if you see an red PlayStation store logo icon, that means you've purchased the content
Okay I found account managment my account and it lists three games I've puchased - Final fantasy 7, Chrono Trigger, and FFVI, when I'm in there it says "download" next to each one of them, do I need to connect my psp to my PC to do this?
No you don't need to connect to your PC, just make sure your Vita or PSP is connected to your WiFi, or you can download them to your PS3 and transfer them that way.
Feel free to add me as a friend. Just put "playstation forums" in the friend request.