This post is part of a series:
1. Write and polish a short story.
2. Research the short story market.
3.Make a list of appropriate markets, and begin a submissions record.
4. Submit the story to the first market on the list, and keep submitting.
Here's the most important thing: read the submission guidelines. If anything I say here contradicts the submission guidelines, follow the submission guidelines.
Submitting manuscripts is easier than it's ever been, thanks to electronic submissions. There's no rush to the post office, no SASE...just a few clicks of a button. Some magazines have an online form to fill out, but if they ask for an e-mail, here's roughly what it should look like:
SUBJECT: Submission: Story Title
I've attached "Story Title," a 3,000 word science fiction story. Thank you for your time and consideration.
If you have any fiction sales, you should include that ("My fiction has appeared in X, Y, Z"). Most magazines ask for attachments as a .doc or .rtf, with the story in manuscript format or some stated variant of manuscript format.
After submitting the manuscript, I highly recommend trying to forget about it. Write something new. Keep going. When the response comes, you can either cheer or submit it to the next market on your list. Why submit it again, someplace new?
Editors have different tastes and different needs. Once upon a time when I was reading slush, we got two zombie stories at the same time. We published one. We didn't take the other, because we already had something similar -- not because it was a bad story. There may come a point to stop and edit the story again (which would be an entirely different post), but rejection letters are normal. They are common. And they never seem so bad, when there's another market to submit to.