I don't know how you become an extra, but don't you also have to be a member of the Screen Actors' Guild? They're unionized, y'know...
No, you don't have to have a SAG card to be an extra. Generally you go through local talent/modeling agencies. Casting directors contact the agencies to send over talent; oftentimes, they will post an open call for extras in the "Auditions" section of the local newspaper. Some casting companies have toll-free numbers with recorded messages on auditions and casting calls, but if you are listed with an agency, you will get casting call notices every-time a production is in your area, and your "type"(sex, age, etc.) is needed. These are generally unpaid positions, so SAG does not factor in.
By the way, I really got a kick out of your thread. These people are pathetic. I don't know whether to laugh or feel pity. I would think that some of these people don't have enough functioning brain cells to dress themselves, so I am hoping that I would not be subject to running into them on the street. Now that is a truly **shudder** scary thought.