Go to the library and pick out publications that publish stories similar to yours. You can also go on the Internet and research publishers that might fit your type of story. Pick out a few that you think would be a good fit.
Study the publisher carefully. If your story seems suitable for them, check out their archives or back issues and get a feel for what they publish. Find their writer's guidelines and read them thoroughly. Many publishers want very specific things and will note that in the guidelines.
Prepare a cover letter with a good opening paragraph in order to get the editor interested. Continue on with a short description of your story, as well as any information about yourself, such as other publishing credits. End your note thanking them for their consideration. Be sure to include all of your contact info so it will be easy for the editor to contact you.
Submit your cover letter and manuscript (depending on the guidelines) to the editor. If submitting by postal mail, include a SASE (self-addressed stamped envelope) in order to receive a response back.
Create a journal or database on your computer in order to track your submissions. Include categories such as: publication sent to, date submitted, response time, date accepted/rejected and any notes you may have about the publication.