Moving into the Side Control position I briefly discuss the different type of hand grips and body positions in Side Control. I then explain how to get into the "one pec theory" position and how to maintain control.
After discussing how to maintain control I show a basic submission, the Paper Cutter. This submission relies on good body pressure and when you practice this you should remember to roll up onto your opponent and never let your hips or knees touch the floor (for the setup).
Make sure that you lift their head and shoulders off the ground when you roll up onto their body, this will give you a little control over their hips so that you don't get bridged off.
Also remember to enter with the thumb down (reference the video) and then close the fist into the thumb up position. This will grant you an extra few inches on your grip and can mean the difference between getting the submission or having to transition instead.
If you drop your elbow and lay on your butt cheek and your opponent is not immediately tapping then you need to transition to another position. This hand grip is very difficult (or impossible) to tighten up after you've switched your base and chances are your opponent is not going to sit idly while you switch back and try to readjust.