First, check the spelling and grammar of your piece. Do NOT rely on your word processor's spelling/grammar checker to do this for you! If you type "Jenny was Eric's best fried in high school", the spell checker won't catch the misspell in the word "friend". But you can bet the market editor will catch it, and they WON'T be impressed. If you've looked the story over a hundred times or you're not comfortable with your level of skill in grammar, ask a friend or a writing partner to look over the story for you. A fresh pair of eyes will see mistakes you've overlooked.
Now that you're relatively sure everything's spelled and said correctly, go over your prose and look for passive words and phrases. "Ellen was singing" can easily become "Ellen sang". Also look for words like "that" and "had". Cut as many of these as you can. The same goes for words ending in -ly. KILL YOUR ADVERBS!! This will make your prose cleaner and tighter, and read faster. The vast majority of editors out there are looking for a quick read.
Now take a look at the story as a whole. Is there a beginning, middle, and end? Can you summarize what happens in a few succinct sentences? Are your characters believable?
Once you've completed these steps, it's time to format your piece. Most markets call for "standard formatting", which (loosely) consists of these rules: