Consider what kind of writing appeals to you, since not all genres suit every temperament. Start with hobbies and interests that could serve as springboards for magazine articles, essays or inspirational poems to strike an editor's fancy. Remember, the more specialized the subject, the more research you'll have to do.
Visit the library for appropriate reference books and materials to sharpen your focus. When you're starting out, nothing feels more inspirational than seeing how others reached the same goal. Consult specialized reference guides like "The Writer's Market" for whom to approach, and specific editorial policies.
Join a local writer's group in your area, if one exists. You'll get accustomed to reading your work aloud in a low-key setting, and hearing feedback from like-minded people--as well as tips about relevant contests, conferences or markets.
Choose a subject that strikes your fancy and see if you can fashion it into an article, essay or short piece that fits the market you wish to crack. Have a clear idea of the destination before you start, or else you're producing something that may never leave your desktop.
Never submit anything without carefully studying the magazine, newspaper or journal--if it's not available at the newsstand or the library, visit the relevant website, or order a back issue.
Revise extensively before submitting to a magazine, newspaper or website--the closer your work seems to a finished product, the more professional you appear. Read your work to other people, and don't be afraid to take their ideas on board. The goal is to eliminate whatever reasons an editor may already have for rejecting your work.
Prepare a query letter outlining why your piece is suitable, the expertise you bring to the subject, and other basic details, such as the word length. Nowadays, most queries can be emailed, but pay attention to specific policies--for example, if the magazine you're approaching frowns on simultaneous submissions, don't risk their ire by trying it.
Avoid taking rejections personally. Your piece may not have fit the magazine's editorial format, there may be others out there like it, or it lacked the "wow" factor to pry open an editor's checkbook. Whatever happens, try to learn from the situation. Most editors will give their feedback if you ask for it.
Don't neglect the copyright basics once you do sell your work. Writing is like any other business, and should be treated accordingly. Avoid submitting on speculation--this means you won't see a dime until your work is accepted. Strive to keep your reprint rights, so even if someone else holds the copyright, you can still make money selling your piece elsewhere.
Keep careful records of submissions and payments. Consult an accountant or a tax attorney to evaluate your legal position, since the requirements for self-employed people differ greatly from their regularly-employed counterparts.