"Writing is not like painting where you add. It is not what you put on the canvas that the reader sees.
Writing is more like a sculpture where you remove, you eliminate in order to make the work visible. Even those pages you remove somehow remain."
- Elie Wiesel

Those are some very wise words from a person I've never heard of before but for this very astute observation. (Sorry, I'm still young!) But this idea should really be expanded upon.

Writing is very much like a sculpture. In your first draft, you collect your ideas and throw them onto the paper (depending, of course, how you like to write your first drafts). Then you slot them together into something cohesive, until you have something vaguely representative of a story that goes from start to finish. That might be your chunk of clay, in the general shape of your sculpture.
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So now that you're up to your second draft, how do you approach it?

In steps, that's how! At each step you will go through your manuscript once and focus on just one aspect. This makes revision much more manageable and structured.

First Pass
This is the first stage of revision. At this stage, the story truly begins to take shape. You go through and edit for content, change any details you want, and make sure they're consistent. This is also the stage where you will rewrite any scenes that have been niggling you from that first draft.

Now you have smoothed out the form of your sculpture.

Second Pass
Go through your manuscript focusing foremost on characters. Make sure the way they act is consistent throughout, or that a change in them remains later on and that they don't switch back and forth between personalities. Importantly, check that their character voice is consistent. Do they speak with more or less contractions? Do they use shorter sentences, or do they tend to drone on? Do they say the word "that" when unnecessary, or do they leave it out where possible? Are they well-spoken? Gentlemanly or sour?

You've now carved the face into your sculpture, and it's smiling at you.

Third Pass
Here you will focus on the description in your manuscript. You want descriptions that are strong, that give the reader an image. You don't want to go overboard, though. We don't want to know about the flea unless it's pivotal to the story. Again, check for consistency. You don't want anything to have suddenly moved from one side of the room to the other.

That jacket on your sculpture is sure looking fine today!

Fourth Pass
Just read through here and check that things look fairly good in general.

You step back and take a breath before you jump back in one last time.

Fifth Pass
Now it's time for the line edits. This is where you go through the lines one by one and make the writing nice and shiny. But if you notice there's more to do from one of the earlier stages, back up. If it's major, deal with that first. If it's minor, touch it up and move on. When you get to the end of this stage, you've done your first revision.

You brush the dust off the top of your sculpture's head and all the details seem to suddenly come to life. But you want to sell this - this is going to make you famous. So like any good artist, you approach it once more, striving for perfection.
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As we all know, perfection is impossible. But make something as good as it can be, and you've got a good chance at being successful.

For a more basic breakdown of the steps, go here.