Got my first sub, a Kimura in the very beginning of the second round.
If you go to the tutorial and then Submissions it will take you through how to pull off the sub.
It says initiate the submission, then either tap square, circle, X, triangle or rotate the right analog clockwise as fast as you can, then it locks the submission in, then you have to tap or rotate again as fast as you can, and if you "succeed" you will pull off the submission and get the tap out. I say "succeed" because it seems so random, I can tap or rotate like a mad man on a severely damaged Chuck and still get reversed... oh well.
This game is awesome as hell though, glad I reserved it a while back. And although Shogun is my boy... I absolutely LOVE to GnP in this game, so I'll probably be GSP often, so I can pound face more efficiently.