Escape the back - safe side
Basic back escapes are broken down into three categories: Safe side, risky side and scoop. When performing safe or risky side escapes you move in a lateral direction relative to your partner. They are both done when your partner has one underhook from the back. When you escape towards the underhook, it is considered a safe side escape. When you escape away from the underhook it is considered a risky side escape, (as you are moving into the choking or striking hand). The scoop escape is performed when your partner has no underhook control and you escape towards their feet.
Before we get into the escapes, lets look at the basic choke from the back. After all the classification of defenses are based upon which hand your partner attacks with.
This first step to performing the safe side escape is to crunch forward, away from your partner, in an attempt to break the chest/back connection. The degree to which you are successful breaking the connection will determine how you proceed. We will start with the ideal escape for the person defending and then move on from there.
Beginning your escape by leaning forward is ideal however it doesn't always happen. If your opponent over powers you or establishes a solid control before you begin your escape, you will need to go with their energy and escape towards their head. You could just fall to your side and begin escaping, in my experience though if you generate a little momentum first by moving towards their head you have a much higher chance of escaping.
The best escape
Old school advice on escaping went something like this:
Student - "How do I escape __________?"
Teacher - "Don't let ________ happen"
Super not helpful without a corresponding plan of action. While I reserve the right to use the phrase "don't let ______ happen" I do have some specific advice on not allowing your back to be taken.
Anytime you think your back is about to be taken, just put your back on the mat.
One of my teachers gave me that advice when I was a blue belt and it was literally my only back defense, (embarrassingly), until brown belt. It is very easy to do and very effective.
If you put in the back escape reps AND then remember to put your back on the mat anytime it is about to be taken you will be much further down the road than I was.