Technically, edits should begin with a rest period -- usually about 6 weeks of not-looking-at-your-manuscript. This break is vital as it helps you to view your work with fresh eyes.
However, for me, this break needs to come later...at least for short stories. So here is how I like to do things:
1. Read through as soon as I can after I finish the first draft. For me, there are things that I knew were wrong when I wrote them. Ehk, that felt awkward. Mmm, that will need to be explained better. Ooops, that character needs to be introduced sooner. Yikes, that sentence sounds so boring. And so on. These things are best addressed ASAP when I start editing, otherwise they weigh on my mind. I like to print out a copy of my draft (in tiny print but with big margins), read through, and scribble notes in the margins.
2. After scribbling notes in the margins, I feel like a weight is off my chest and I tuck my story away for a day or two. I let my "to fix" list brew in my mind for a little while.
3. Sometimes, I read an article on editing. Go Teen Writers is usually helpful for me. If you imagine my edits brewing in my mind like a tea, then casually reading through editing tips is like adding some fancy leaves to steep in my cup.
4. Work through my margin notes. This is where I am in the process right now. I just finished Chapter Two last night.
When I finish fixing my margin notes, I might take another short break. Then I will pull out some editing tips in earnest. Instead of casually reading them, I will take each step and apply it to my story. I'll look for unnecessary words, character breaches, dull scenes, etc. When I get it as far as I can, I will then turn to my critiquing friends. They will catch all of the things that I could not see.
Somewhere in here will be a 6 week break...maybe longer. And then I will come back to the story and see how far I can get with fresh eyes.
But all of this is far ahead of me. For now, my goal is to fix Chapter Three by its margin notes before the weekend.