I'm not going to fool you. Micro-level editing requires a lot of time and patience. There's really no way around it, so deal with it if you want to be published.
Micro-level editing involves the minute details of your story, whether or not a certain word should be there or a certain sentence. Those who do not write have little appreciation for this, and frankly don't understand what a single word could mean to the entire story. But for us writers, we do. We know. Like the skilled cabinetmaker, we sand down all of the corners, even if they won't be seen. (Words, however, are seen of course . . .)
Take this for an analogy. Michelangelo paints the Sistine Chapel, so exquisite and complete that from the floor it's as beautiful as ever. But up close, here and there, the work is sloppy. Very small places, he does this. What happens? The Sistine Chapel isn't as exquisite as you thought. That's why the smallest details can make or break the story.
Break your story into pieces. First, lump your chapters together. For example, in my thriller Beholder's Eye, I lump the first nine chapters together and call them "The 1st body." This is for my own organizing, I didn't really name this "Part 1: the 1st body." No way. Then, I take each chapter and break it down into scenes, which is easy because it's usually where the page break is. I examine each scene as a whole, reading ever-so slowly, with my mind whirling.
Does the scene make sense? Do the characters advance, even a little bit? Is this scene necessary to further the story? Is the dialogue realistic-sounding? Is some of the dialogue unnecessary? Could my descriptions get beefed up a little--try three or four good non-cliche descriptions, ones that will make it unique? Speaking of cliche, are there any cliches, either in the dialogue or the scene itself? Do I have any unnecessary adverbs--or have I eliminated them altogether? Is the dialogue simplified to be "he said" and "she said."?
Even the use of a repeated word can cause a reader to draw attention to the words instead of the story. I was recently editing Beholder's Eye and found in two paragraphs I used the word "after" three times. Carefully examining these two paragraphs, I eliminated two of them--one I completely struck from the story and the other one I re-worded.
This should get your started, and by no means is this a complete list.
Remember: above all, have patience. Your story will be worth it.