The Editing Process

Editing my own works isn't something I do very well - I read things over of course and make the odd minor change, but I've never done a proper critical edit of my fic. I want to improve my writing though, and I've got a couple of fics in the pipeline that I hope have the potential to be really good, and good editing is going to help a lot with that.

So, I thought I'd see what wisdom all the brilliant writers on here have to share!
What do you look for when you edit (or beta!)?
How does your editing process (or beta process) work?

Any thoughts are massively appreciated!