Begin the process of getting published by doing research on publishing markets. Through reading, you'll get a sense of what is being published today and where your work fits in.

© 2006 Ginny Wiehardt.Haunt a bookstore with a good selection of literary magazines. Read a few; consider subscribing to ones you particularly admire. At the very least, check out the websites of journals you are considering. Find out where writers you admire were published in the beginning of their careers.
Next, pick up (or check out from the library) a copy of
Novel and Short Story Writer's Market, which includes descriptions of thousands of literary journals and magazines, with names of editors, reading periods, addresses, and brief descriptions of the kind of work they publish. Using this resource and the journal websites, you'll find the information you need to
submit short stories in a professional manner.
Finally, if you're also applying to
contests, do your research with a healthy awareness of scams. There are people out there ready to take advantage of your desire to be published; become familiar with the most common rackets.