Jaysmackz brought this up on another thread and I figured I'd start a new one, just so that this could be a little more obvious and be in the right place.
The question is what to do when you get his arm and guard.
First, plant his arm in a position that he can't get out of. I like to put his arm under the armpit of the opposite arm (so if I'm looking for a right-side armbar, I slip his wrist under my right arm).
Then sweep the leg of the side you're baring (sticking with the right-side armbar, use the left leg) over his head against his face. Then hang onto the arm while you arch you back hyperextend the arm and/or break the capsule in the shoulder.
Some people find that it's easier to keep the foot that will be under the arm out of guard and push off of the ribs with your shin/ankle, which helps to tear at the should and give leverage. If you watch Rickson Gracie, this is how he does it.