Prepare your ideas. Although you don't need to know everything about your story before you write it, you at least need an idea, a plot, a character--something to base your story around.
Write your story. Don't allow yourself to get stuck. Many stories never get finished because the author gets writer's block. The best way to avoid this is to force yourself to write, even if what comes out isn't very good--you will clean it up in the editing stage.
Edit your story. Make everything make sense and correct any spelling or grammatical errors. Don't be afraid to cut or add large sections of text. Sometimes a story will need a massive overhaul.
Research places to get your work published. Look at publication houses for large stories (novels and novellas) and magazines (both literary and popular) for short stories. Make a list of publishers that publish the type of story (nonfiction, fiction, fantasy, horror etc.) that you have written. Sending your work to the wrong publisher will guarantee that it will not get published.
Send your story to your potential publishers. Most publishers take electronic submissions, so you may not need to worry about the standard mail. Make sure to follow the submission guidelines as well as possible. If you are sending to publishers that accept simultaneous submissions, you can send your story to several publishers at once. This is the best way to get your story accepted in a timely manner.
Keep sending your story to different publishers. It sometimes takes several tries to get published. If you believe in your story, don't give up.