How should I approach rewrites?

In a blog post from 2005, John August has this general advice:

Decide out what you want to accomplish, then figure out which scenes would need to change.

The first instinct of a lot of writers is to start from the beginning of the script and look for dialogue blocks, action lines, or description to improve. These are good, but rewrites can do more than that.

Try establishing bigger picture goals for the rewrite. Look for relationships that need strengthening, plot points that can be improved, or extraneous beats that can be eliminated. Identify the scenes that can be adjusted or rewritten to help you accomplish your goals. Then get to work.

Rewrites should not simply make pieces of the script better; ideally, they should make the script on the whole fundamentally better.

Of course, it never hurts to look for little tweaks and places where you can save page and story real estate, too.