You did it. The last word of the last sentence of your story is written, your i's have been dotted, t's crossed, and your pen is down. Congratulations! You have a completed short story! Now what do you do with it?
If your aim is to get your story published, then your best bet is to submit it to literary magazines. Submitting can be a daunting prospect, but never fear - here's a guide that will take you through the process step by step.
Step 1: Anaylze Your Draft
Before even considering where to publish your story you need to ask yourself these questions: Is this draft complete? Does this story have a proper arc with a beginning, middle and end? Does the character grow (or choose not to grow) by the resolution phase of the plot? Also, have you edited this story? Have you had someone else edit it as well with fresh eyes? If not, then you are probably still in draft phase and not final copy phase.
Publishing a short story might be a one-time event for you, but that doesn't mean you want to treat the process any less professionally than you would your normal job. Publishers do not want to see things riddled with typos, mistakes, or sentences with unclear syntax. They also don't want to read stories with glaring plot holes (like why didn't they use the car sitting in the garage the entire time if they needed to escape?), or inconsistencies in plot or character (this is my stoic main character who never smiles and has no friends but apparently is fantastic at dinner parties). They want a finished story, so give them one.
The bottom line is, don't waste their time or your manuscript is going right in the trash can.
Step 2: Identify Your Market
Literary magazines (or lit mags) generally run by genre and subgenre, so you need to know walking into your search what your market is. Your market isn't necessarily only a genre, but the audience you think will want to read your piece. If you wrote fantasy, is it High Fantasy, Urban, or just Magical Realism? And, who is your target; are you looking for old readers, young ones, or young fiction that adults can also enjoy?
Once you know what you're writing and who you are targeting you still need to search through the rich cornucopia of magazines out there. For that you want to find a listening site. The best one is the irreplaceable duotrope.com, which now requires a 50$ a year fee but I maintain is every writer's best friend. Absolutewrite.com and Newpages.com will also give you good general listings of mags.
Remember to start small. If you're a new writer you aren't going to be gunning for things like Clarkesworld or The Atlantic. Find a few mags that look like they're at your level - if you aren't sure, their websites will often have samples of what they want, if not online back issues.
Step 3: Submit!
Remember when I said that publishing a short story needs to be treated professionally? That attitude is really important at the actual submission phase. Most mags have very specific criteria for how they want submissions sent to them. Follow their format. Do not sent them a manuscript in bold 14pt comic sans. Do not submit multiple stories if the listing tells you not to. If they want a query letter, do not beg, command, or otherwise cajole them into publishing you.
Small time publishers have a lot of work to do, and their work does not often yield much in the way of thanks or money. They don't want to work with writers who cannot follow rules. Those rules are in place to make a publisher's life easier, so respect them.
A lot of magazines now take online submissions through submittable.com. It's a very useful tool and it will also keep track of who you have submitted to and when. The account is free, so it behooves you to get one.
Step 4: Get Ready For Rejection
No matter how good you are or how long you have been writing, you are going to submit to a publisher and get rejected. You are going to get rejected often. Sometimes this isn't even because your story is bad; it just didn't quite fit with the theme of the publisher's current issue.
If you get rejected, don't despair! Charles Dickens got rejected, so did Stephen King. And me. And your Aunt Hilda. In fact every published writer in the world has likely been rejected by a press at some point in their lives, so you're in good company. Just go down your list of publications and try the next one. You'll get a yes eventually.