I know this is a no-brainer, but it really is the crucial step number one of any publishing attempt. If an editor tells you not to put your name on the manuscripts, any appearance of your name on it will cause the editors to throw it in the trash unread. You're just wasting the cost of postage if you don't read the submission guidelines on the magazine or contest's website.
Use standard everything in your document.
Generally, editors aren't impressed by flashy fonts, and they request double spacing for a reason - readability. In order to make your story as readable as possible, don't use anything but a standard font such as Times New Roman, Helvetica, Verdana, or Arial. Double-space your document so the readers can move easily through your pages. Number your pages.
After the jump: more tips for polishing your presentation.
Here's where your trusty Writer's Market can come in handy. Rather than addressing a vague "To Whom it May Concern" or "Fiction Editor", you can look up in your Writer's Market who the submission is actually supposed to go to. Address your cover letter and your envelope to that person: it's a nice personal touch that may even enable you to skip a level or two of the slush pile.
Remember your SASE.
Editors have hundreds, if not thousands, of cover letters and stories to go through. If you forget your SASE, they're not going to take the trouble to email you or craft a new letter and envelope with a rejection. Don't start on a bad foot by annoying them; follow the rules and have your envelope stamped and addressed.
Keep your cover letter relevant.
In my cover letter, I generally don't try to sum up my story or provide a lengthy synopsis. It's fine to include a sentence describing the main conflict (and hopefully providing a tempting taste of what your story will contain), but more than that is excessive. Instead, give a word count, a list of your past publications, and a quick thank-you for the consideration. If you'd like to see what a cover letter should look like, take a look at the sample letter I made.