Getting the Writer's Market book is great advice.
If you live in a city with a lot of neighborhood newspapers, I'd strongly suggest you start there. I'm a decently successful freelance writer, and I began by checking out the neighborhood papers, seeing what kind of articles are there, and following that lead.
The very first article I wrote was about a local cemetery that had some interesting people buried there. There were free tours, so I went on one, took notes and a few photos with my basic digital camera, and wrote an article suitable for Halloween, which was 6 weeks away. I wrote about a woman who was famous in the 1920s for holding seances, a man who burned down his own factory killing 100 workers, the catacombs there where "animals" now lived but sounded like people crying, etc. I wrote not like a reporter, but as if I were speaking, and included information about the free tours open to the public. I sold it for $100 to a local paper.
My best advice is to just do it, check your grammar, write as if you were telling a story, and if possible, go to the office of the newspaper and tell them you have something they may be very interested in (IF it's a small local paper. Don't do this with larger newspapers/magazines).
It worked for me, and I've since written close to a hundred published articles over the last 5 years.
GOOD LUCK!!!!!!!!!!!
