In LA, you don't need to be a SAG member to be an extra, but you get craploads of benefits and better pay if you are.
If you go through an agency, you get scheduled and paid through them as well. However, the vast majority of extra placement agencies are really poorly run and very lax with their payments and not very aggressive with their placement, so you have a lot of harassing to do on your part.
Your other choice is to go through one of those ads in the paper and sign up directly, but your pay is generally a pittance, you get crappy food, treated like cattle, and there's a good chance you won't even end up in the final cut.