Completing a piece of writing is a satisfying act for writer, and seeing it published in a literary magazine fulfills the writer's goal of being published. Compared to other publications, there is a smaller audience for literary magazines, so there is more competition for pay. For a serious writer, sometimes being published means more than getting paid for the piece, especially at a good publication that can help promote the writer's work.
Read literary magazines and blogs. This is the best way to become more aware and updated about the happenings around the literary community. In these magazines, you may also find information on how to develop your skill as well as a listing of magazines who are currently looking for submissions. You don't have to subscribe if money is an issue. You may also gain experience by becoming involve in college literary magazines that don't pay, but are good starting point in your career as these magazines are not only read by the student body, but by the faculty as well.
Learn writing techniques and develop your skill. Getting published is competitive, so you have to be on top of your game and present your piece effectively. With enough discipline and patience, you can learn effective writing skills on your own. You can also learn these techniques by utilizing the talents of those around you who are already successful writers and teachers, or taking online courses (see Resources below).
Connect with the literary circle by going to events, conferences, poetry readings, etc. If your circle of friends consist of the same people you went to college with who dream of becoming published, the best way to expand your circle and meet people that could boost your career is by networking constantly with the literati. Events are usually held in urban centers, museums and bookstores, especially when a popular author is on tour for a book signing, but libraries usually have regular events as well. This is your chance to build your book of contacts that consists of renowned authors as well as experienced publishers and agents.
Look up magazines on "Writer's Digest," which provides a listing of magazines as well as the various criteria that these magazines require of a piece. This include information about the format, the contact person as well as the pay. "Writer's Digest" gives a brief but informative descriptions of magazines, from commercial to trade magazines, that you will find useful when querying a literary work (see Resources below).
Know how to pitch your piece. Query letters are important because they give the first impression of your work to an editor, so it is necessary to learn how to write a comprehensive and persuasive query letter. The processes usually takes a couple of months, from the point when you pitched your piece to the piece's publication date, depending on the magazine. If you have a contact person in the magazine of publishing house, be sure to contact them as this may be beneficial not only to speed up the process but also increase the chances of your query's acceptance (see Resources below).