When you find yourself held down with the most common and basic forms of control like side mount, you should focus on using the most common and basic forms of escape such as shrimping back to guard, or using the underhook to come up and reverse the position. As you progress in Jiu Jitsu, you will often find your opponents will use other variations of a given position that will thwart your most common forms of escape. When this happens, it is necessary to develop the ability to recognize when you must use alternative methods to escape a particular position.
Your most valuable tool in escaping any position is your ability to recognize what is keeping you down. It is almost impossible for your opponent to control your entire body all at once. Some positions are far more difficult to escape than others, but there is always an opening for escape no matter how your opponent may be controlling you.
The sidemount is a simple way to illustrate this. Your opponent can only control and immobilize either your upper body or lower body at one time, but rarely both simultaneously. Similarly he can only control one side of your body at a time, but almost never both. When you want to escape, your first goal is to recognize what is holding you down and then work towards freeing that part of your body or finding the opening your opponent is giving you and exploiting his lack of control.
In this video below, we go over some of the variations of the side mount you will encounter and how to escape each one.