That is a question I get all the time.
The answer is easy: Perseverance.
The implementation is the difficult part.
In order to get a story published, you first have to submit it for consideration. Crazy, I know, but until your pen name is a house hold word, people don’t come looking to you to give them stories. Even then, most still won’t.
Currently I have 10 short stories under submission to various places. (Actually, I may have more. Sometimes I lose track of them for a month or two. *sigh*) If one gets rejected, I turn right around and submit it somewhere else. It does me no good if it is just sitting on my hard drive.
The exception to that is when I get a personal note on the rejection. These are good! Trust me. An editor who does that liked something they saw in your writing! (Unless it is really just a freaking nasty note, in which case you didn’t want to be doing business with those people anyway.) Always take any personal note sent to you seriously. Pay attention to it. Weigh it. Decide what it means. If it applies, you might want to re-think and re-work that story.
Then, send it out again! There will always be new markets to find somewhere, and you never know which is being edited by someone who sees that story exactly the way you did– Perfect!
But where to send the stories? Where to submit?
There are many different ways to do this. Two of the most popular are DuoTrope and Ralan. You can use these to search for markets to submit to. You can also use Google, Yahoo, or whatever your favorite search engine is. Not everything ends up on a list, so I recommend doing that occasionally.
Also, be in touch with your local writing community. Watch for local publishers/authors who are doing anthologies and try to get in them. This is where you will start down the path of people asking you for stories!
My personal commendation is to start with professional rate paying markets (6¢ per word or higher) and work your way down the list. You don’t want to give away a story for free when you could have made $2,000 on it! (2k! Really? Are you kidding? — Chances are seriously against it, but there are some markets that pay that well. If your story fits what they are looking for, what have you got to lose? Here is an example at Tor books.) The exception to this, for me, is when I write the story for a specific anthology. I really want to give people I know the best story I can even if they aren’t paying pro-rates. They are the ones who have helped me build up my career, and I want them to keep going in theirs!
Getting published with a short story is not hard. It just takes time and effort. Getting published at a pro-rate is a bit harder, but you can do it!