The 'escape' will be dependent on how the person is holding you down in side control.
Your escape will be based on where their hands and weight are in relation to your body.
If your opponents hands are on the same side of your body, say for example their hands are on your the left side of your body and your opponent is lying on your right side, a shrimping/snaking movement might do the trick. However, if your opponents hands are on the right side of your body and your opponent is lying on your right side (he has a cross face on you and is pinning your hip), the shrimping/snake movement isn't going to help. It depends, there's a lot of things happening even though there doesn't look like a whole lot of movement.
The bottom line is if someone can isolate your shoulder girdle to the mat and 'pin' you down, you won't have the luxury of movement and thus you'll be 'stuck.' A good rule of thumb is NEVER, EVER be flat on your back. This will give you some flexibility with movement and will present some options. (Maybe not good ones, but at least something)
Of course, the best way to learn about escaping is to get some instruction with a qualified instructor, but if that's not an option, there are several good video's on the market that can help. The Joe Moriera white/belt video's by Panther are very good. Joe's a good guy and a very good instructor. He presents information in sequence. Of course, there are many others that are very good, Micheal Jen's Ultimate Pin escapes (www.teammaa.com
) are excellent also. I've trained with Michael and his instruction is also top notch.
Good luck with your training.