Every book I write goes through the wringer. After the first draft is done, I go back through it numerous times to check for grammatical errors, continuity errors, etc. So in case you think you've finished writing once you've gotten through that first run, here's what happens next.
It's done! Drink a toast or go to dinner. Finishing up the story is an accomplishment in and of itself. Lots of people don't get that far.
2. Take a break
Your best bet at making this something good is to provide some distance. Jumping right back into edits will only ensure you're missing the same mistakes you've already made. You become "word blind" to the same misspelled or misused words. You're still so involved in the plot that you miss obvious plot holes.
3. Hunker down and put your editor hat on
My next pass is for continuity and copyediting. Does everything follow? Did a character change his name between page 2 and page 200? Are their names spelled consistently? Are there any time warps? (i.e., it's morning when we are in one POV, but in the next section its the day before or two days later?)
4. READ THE WHOLE THING, start to finish
I do this multiple times, each time looking for different things (reference point 3). Once I'm satisfied that the holes are filled and everything is "right," I read the entire book one more time for all the things I've overlooked, or new mistakes I've made in the copyediting process. You'd be amazed at the number of things that STILL jump out at me, even after I'm sure I got it right "this time."
5. Culling out overused and unnecessary words
With time, I get to the point where I recognize a lot of the "crutch" words and can kill them during the creative process, but they still pop up. (Can I get an amen to the word "still" which I have used too many times in this post?) I have a checklist with words like "just" and "maybe" and distancing verbs like "could see" or "felt." Granted, some of them belong, but the majority of them are superfluous and take away from the reading experience. I save this step for the last, because while I'm copyediting, new unintended occurrences can pop in. Oh, and then I repeat step 4. Any time I edit, there's always the chance I've created new mistakes while correcting existing ones.
This process works with most every book I write. There are exceptions, and those books are generally the ones that either don't make it to the editor (they aren't fit for public consumption - yes, I have a couple tucked into my "even I don't like this one" folder) or ones that I do love, but there's "something missing." The latter requires extra work, extra thought.