What you need:
Vita with OFW (I used 3.12)
PS3 with CFW (mine had 4.46 Rogero 1.00 Cobra when testing)
PS3 System File Editor 0.80
a WiFi router (best if it's connected via cable to the PS3, not wireless)
any PS3 game backup
1. D/L & install PS3 System File Editor on your PC.
2. Open the directory of the PS3 game backup you want to enable remote play for, and locate the PARAM.SFO file (in PS3_GAME folder or USRDIR).
3. Backup the PARAM.SFO file.
4. Open PS3 System File Editor (ignore the warnings) & load the PARAM.SFO file you want to modify.
5. Just tick the box under Remote Play & save the file, overwriting the original (make sure it's backed up first).
6. Pair your Vita with your PS3 (locate remote play on either device and follow the instructions).
7. Launch Remote Play on your Vita and connect to your PS3 via private network (the system will guide you on what to do, internet should work also but is NOT advised with CFW PS3, since it requires PSN).
8. You now control your PS3 through your Vita, launch MultiMan (or whatever you use to launch game backups) & load the game for which you modified the PARAM.SFO file.
9. Launch the game from the XMB, via the Vita.
10. Presto, you are now playing via Remote Play on your PS Vita!
Keep in mind you have to edit the PARAM.SFO file for each game separately, but once that's done, you're good to go.
Also Not All Games Work. I Made A List of Games I Have That Work.
Also, I highly recommend NOT to allow your PS3 to connect to PSN, since this method requires a hacked console and you run the risk of being banned!