Spell check. You might also want to look over it and see if anything sticks out in your mind.
See if there's anywhere you could have showed instead of told. For example, if you wrote "He was angry," try "His fists were clenched, his face like a time bomb" or something like that.
See if there are any places where you could have removed the word "and" and started a new sentence. For example, if you wrote "He passed me a cigarette with trembling fingers and then folded his legs to sit down beside me," try "He passed me a cigarette with trembling fingers. His legs folded as he sat down beside me." It is almost always stronger and hits harder with the reader.
If a sentence ends with a preposition, see if you can rework it. We all do it, but sometimes it sounds weak. For example, "I scanned the room for a chair to sit in" could be changed to "I scanned the room for a place to sit."
Take out all unnecessary words. If it doesn't forward the story, doesn't show action and doesn't enhance the character, atmosphere or plot, it doesn't need to be there.
Get someone you trust to read it and let you know what he or she honestly thinks. Another good suggestion is reading it out loud to see if it flows. You'd be amazed the snags you detect when you do this.
Get rid of all unnecessary emphasis. Fan fiction tends to be littered with *stars around the words* and CAPITAL LETTERS ALL OVER THE PLACE. Use a simply _ on either side of the word to indicate italics. Italics should be used sparingly. If you find your story marred with emphasis, find a way to restructure the sentence so that the words work on their own without *stars* or CAPITAL LETTERS. CAPITAL LETTERS ARE IRRITATING. JUST IMAGINE IF THIS WHOLE PAGE WERE WRITTEN LIKE THIS. WOULDN'T IT FEEL LIKE SOMEONE WAS SHOUTING AT YOU? *YES*, IT WOULD.