Teaching all of the expression editor would mean teaching you how to code, and how to use mel.

Mostly the expression editor is used for automating things.

Such as:
sphere1.translateX = sphere2.rotateX;

This would make sphere1 translate in the x direction, when you rotate sphere2 in the x direction. If sphere2's rotate x value is 120, then sphere1's translate x value is 120.

If you ask a more specific question, I'll be able to help you out further.