A chronological explanation of the best way to get your short story published
Make sure that you have written a story that is worth publishing
The first step in getting a short story published is of course to write a publishable short story. Try reading well regarded short stories from master writers to get a sense of the appropriate scope and plot development of a short story. Plotting, grammar, spelling, and so on all need to be in good shape.
Have others read the story to help you do any final adjusting
Try testing your short story with an audience. Have a friend, roommate, or family member read it and point out any inconsistencies, plot holes, or other weaknesses. Make sure they can follow what you were trying to accomplish with the plot.
Think about the type of venue that would be well suited for your story
If you think you have a good, publishable story, you need to decide where to publish it. There are thousands of websites and magazines that publish short stories. For a novice author, expect to publish in a non-paying magazine or website. If you want to make money by writing, you need to work your way toward the big publications.
Consider options such as niche publications or writing contests
If your story has the potential to be interesting to a niche audience, you can try to find a venue to get it published that appeals to that niche. Alternately, you could try to enter the story in a contest. If there are entry fees for the contest, do due diligence to make sure the contest is reputable and legitimate.
Compile a list of magazines and/or websites to which you will submit the story
Compile a list of venues that might be suitable for your publication. Google has a fairly comprehensive list of publishing magazines, as does the Novel and Short Story Writer’s Market. It is a good idea to read at least on issue of a publication to make sure you understand the style and that it is well suited as a publication for your story.
Get your submission packet compiled for each publication
Prepare the packets for your submissions. Purchase manila envelopes for each publication to which you are submitting, as well as self addressed stamped envelopes for their responses. Write a unique cover letter to each publication that gives just a small amount of introduction to both you and the story.
Send your submission to a variety of different publications
Submit the story to the publications. You should send your story to 10-20 publications to give yourself a decent chance of being published. Often, publications will specify that you cannot simultaneously submit to other publications. This can be ignored. In the rare event that two venues accept the story, simply call and withdraw the story from both. If it was good enough for two to accept it, you will likely find a third venue to accept it.