This market can be very hard to break into without some writing experience and quality clips under your belt. Once you do have a few clips though, writing for magazines can be very lucrative. The pay rates vary widely depending on the type of magazine. Smaller trade magazines pay less than national consumer magazines, but they are also easier to get into.
Learning to write a solid query letter is an absolute must in order to break into magazine writing. It typically works by you pitching an idea to an editor. To do this effectively, you need to understand the magazine you are querying, have a feel for its audience, and sell your idea to an editor by highlighting how your work is original and also meets the needs of their target audience.
I highly recommend picking up the latest edition of the Writer's Market guide. Every book gives you a one year subscription to their website as well. This ensures you have the absolute latest contact information, writers guidelines, and list of what publications are looking for. It is very worth the 39.95 price tag. If you don't want a copy of the book, you can also purchase monthly memberships for 5.99. This website/book not only list the writer's guidelines, but also the current pay rates for articles.
Magazine payment terms vary. Many pay upon acceptance, but others do not pay you until publication. Many publications will also offer a "kill fee" in the event they change their mind about running your article. It's typically a percentage of the amount they agreed to pay for the article originally. Once this happens, you are then free to pitch your article elsewhere.
Every contract for magazine writing differs, so be sure to read and understand your agreement fully before signing on the dotted line. Some magazines will insist on "full rights", meaning you cannot ever publish that article again elsewhere, where others may only contract to have exclusive rights for a specific amount of time. After that you can rework or resell your article again.