Sign onto the Internet on your computer. Search in a writers' database, such as Poets & Writers, of literary magazines for those that accept submissions in your particular genre.
Read carefully the submission guidelines and author payment descriptions for these magazines. If they provide author copies or subscriptions only, move on to the next journal.
Bookmark those journals that offer monetary payment for accepted pieces.
Read a few issues of the bookmarked journals to see whether or not they would like your style of writing. Remove from your bookmark list those journals that do not seem like a good fit for your writing, leaving the links to the websites of those that might be appropriate venues for your work.
Create a cover letter for your submission. Include your address and contact information, the date, and the journal's contact information and address. Find out the name of the appropriate editor (fiction, poetry, etc.) and address your letter specifically to him. In the body of the letter, include the names of the pieces you are submitting and a brief biography, including past publications.
Print this cover letter and sign your name in pen at the bottom. Print the pieces that you will submit as well. Attach the cover letter to the front of the written work with a paper clip. Also include a self-addressed, stamped envelope for the editor's response.
Place all of these materials in a large manila envelope. Write the editor's name, magazine's address and your own return address on the envelope.
Place adequate postage on the outer envelope, weighing it at a local post office, if necessary. Mail your submission.
Keep a record of where you have submitted your work to avoid mistakenly submitting the same piece to two magazines (that is, if they do not accept simultaneous submissions).