My code refactoring algorithm

You're looking at a block of Python code. It's not immediately obvious what it does. It's sort of a mess and you realize it needs to be refactored. But how? What mental algorithm do you use?

Here's a trick I just figured out how to put into words. You first add comments to your code to make it easier to explain what it's doing in each part. Then you restructure the code until those comments are no longer necessary, using the comments as a guide to creating high level constructs that not only tuck complexity neatly away, they also explain the purpose of the surface.

What tricks do you use?