First step: Find someone you can trust who is also more proficient in English than most of the people you know- ask that person to proofread your work. A spellchecker won't do the job adequately. If you're lucky, that person will 1) catch what you missed, and 2) be a harsh critic. The more you correct before submission, the better. The thicker your skin when it comes to critique of your work, the better.
Second step: Identify your target market. Given where you're asking your question, I'll assume its fantasy, sci-fi, or horror. Everyone knows about Asimov, Fantasy & Sci-Fi Magazine, and Dragon, but there are many other outlets.
Third step: Do what Whizbang suggested: Writer and Writer's Market are invaluable. Use them to find publishers in your target market.
Fourth step: Submit your work, but be prepared for rejections. Everyone gets them.
Fifth step: Keep writing. You may even find yourself being rejected, but still asked to freelance some stuff. Do it.
Sixth step: If you do get an offer, it will likely be small. Take it and put the experience on your resume. Take the check and cash it. Buy at least one bottle of something alcoholic and celebrate.
Seventh step: If nobody gives you a nibble, you may consider self-publishing, either as print or e-book. While this is rarely considered "being published" by the pros, it will help boost word of mouth- your best friend if you are good, your worst enemy if you aren't.