Hoisted from Facebook:
Q. How should I start looking into getting published?
A. The most important thing is writing. The next most important thing is finishing. The next next most important thing is researching markets and sending things out. If you are doing all that, there are two other great force multipliers: not waiting to start your next piece while the previous ones are out, and networking - going where other authors are: cons, writing conferences, writing workshops. If you are doing all that, get yourself an agent - it is the next big multiplier.
And that's it, in 95 words! Paraphrasing Robert Heinlein, to get published, you've got to write, you've got to finish what you write, you've got to send out what you write until it gets sold. But if you really want to get published, you can't wait on that first piece to succeed; you need to go ahead and start the next one. And you can't rely on your own ability to find opportunities and markets; you've got to find other writers and editors to help you find the right home for your work. And if you're doing all that, you're on the path to having interesting enough work to attract an agent, so you might as well start looking.