Ask a writer friend to read your story and offer edits. A fine-tuned story will have a much better chance of getting published than one that nobody else has ever read.
Research target publications. (See Resources for places to look.) Make sure your targeted publication regularly publishes humorous stories of either fiction or non-fiction. If you are a beginner, stay open to smaller publications that will be more open to furthering fledgling careers.
Read a few issues of the publications you chose. Make sure your sense of humor matches that of your target publication. If your story is raunchy, don't pick a publication that focuses on wholesome, family-friendly humor.
Write a cover letter about one-half page long. Introduce yourself to the editor, outline any previous publishing experience and briefly sell your story. Make sure you spell the editor's name correctly and double check your letter for grammatical errors.
Follow each publication's submission policies.
Send out copies of your hand-signed cover letter along with your manuscript. Include a self-addressed, stamped envelope with your story so the editor can mail back a response.
Make a list of the publications to which you sent stories, along with the date you sent them. This will help avoid re-sending your publication to editors who have already rejected it, if you continue to send your story out to different publications.
Keep trying. Many famous writers have posted their walls with rejection letters before achieving success. Keep asking people whose writing skills you respect to read your story and fine-tune the manuscript to reflect their edits.