First, find the work! Look on local theater websites, find local film companies, read the newspaper classifieds, get in touch with local commercial agencies, production offices or acting agents, and get involved in your arts community. You do NOT have to move to Hollywood to become an extra.
Second of all, you will NEVER have to pay anyone money to be an extra on a movie set. They compensate you. Anyone who claims that you have to pay a fee to "register" or anything else is not reputable.
Be prepared to wait. Whether that be the day that you get seen at a production office, the day you get fitted for a costume (if you need one), the time at which you get your picture taken on the day of the shoot, waiting for the shoot to begin, and sitting on set as you are shooting. The life of an extra is essentially being a professional person who sits around. Patience is a must for this job.
Bring a book, if you're allowed. Otherwise, snacks and sometimes even movies will be provided for you as you wait around. Typically, this is a great job for students because you can bring your homework. There's an upside to all that free time.
When you get on-set, LISTEN CAREFULLY. Don't chatter to your fellow extras, laugh loudly, or cause a stir. You will be kicked off set immediately and unceremoniously.
Do what your director tells you to do. Often times the assistant director will come over and assign you a task while the camera is rolling. It may be your job to dance, to drink a drink, to walk from left to right. Whatever they tell you to do, do it. Don't try to add anything or take anything away.
These are the most important pieces of advice I can give you as someone who has been an extra (My Name Is Jerry) AND the person directing extras (Third To Mars). DO NOT MAKE NOISE and DO NOT LOOK INTO THE CAMERA. These things can ruin the "takes" and also get you kicked off set. Even if you are in a crowd scene, and you are meant to look like you're talking, you will be asked to pantomime. So practice doing so in front of a mirror to see what looks real and what doesn't.
I was taught this by lifetime assistant director Craig Huston at a seminar last December. If you are an extra, stay relaxed. It may not feel like a relaxing environment, but it really is a simple job. If you are doing this as a pre-cursor to professional acting, learn how to act as natural as you can and not to look like you're acting.
If you do a good job, there is always a chance that you could get asked to be what's called a "featured extra". Typically, these parts are decided ahead of time. But if they're not, and you get the chance...just stay cool and pretend like it's not a big deal. Keep your energy up, but don't make an excited scene. People who seem like super-fans or movie geeks may not get handed more responsibility.
Lastly and most importantly, don't stare at the actors, crew, or director. You may be interested and excited...but staring at the people working on set can be distracting.
Show up on time, work professionally, and there's a good chance you could get your name on a list and be called back for more work. If you enjoyed your experience, consider looking for a casting agency or professional representation. It could be your official foot in the door to the world of acting.