The usual way to get started as an extra is to find a casting company or calling service which handles extras (there are many which specialize in extras) and go and register with it.
This means you will make an appointment to talk to someone at the casting company, go in and talk to someone briefly and then hand over some amount of money.
This is unavoidable, and you shouldn't let the fact that the casting company is asking you for a registration fee lead you to assume that they are just a scam or a waste of time.
You shouldn't pay more than about $25. They will actually provide you with services, which range from the simple posting of your picture in a directory to someone making phone calls on your behalf and trying to scare up work for you.
You should try to determine what sort of services they will provide you and judge whether you want to pay the fee accordingly. In this regard, comparison shopping among agencies is probably a good idea, and to save time, try to get as much information as possible about each casting company's services and fees over the telephone before you go in.
When you go in to register, some companies will conduct an interview, while others will simply take a picture, collect your registration fee, and be done with you. If there is an interview the main thing that the casting company representative will wish to determine is: "Will this person give me a sum of money?" They see a lot of people and they need to collect those fees to make a living. However, the person will also determine how serious you are about being an extra, how much experience you have with acting, what special skills you have, and what sort of wardrobe you have. If they don't ask you any of these questions, be wary -- you might be getting scammed.
If you make a good impression the casting company will be more likely to go to bat for you to get you work, so be prepared for the interview. Be ready to mention your good attitude and special skills, and your understanding that being an extra primarily involves showing up on time and staying quiet.
Sadly, some casting companies will pull little side-scams on their registrants, such as referring you to an expensive photographer to get a headshot done (from whom they receive a kickback), charging you an inordinate amount of money to have your résumé printed up on "industry standard" paper, or asking you for "front money" for some project in which you would get to work. These things don't necessarily mean the place is a total scam – it just means they're trying to get a little more money out of you. It can be a good idea to get a headshot done, and it's absolutely necessary if you're interested in getting work as an actor as well, but it's not really necessary for most extra work.
Most extra companies will simply take a picture of you when you register and keep it on file. Similarly, there is an industry standard for the size of paper on which you print your résumé (8X10, so that it can be affixed to the back of your 8X10 headshot), but you don't need a résumé if you're just interested in working as an extra. The point is, if you do decide you want to have a headshot and a résumé, you can probably get these things done much more cheaply if you shop around than if you just do what the casting company tells you. (On the other hand, you should walk out if and when "front money" -- money that you have to chip in to help "fund" a film project -- is demanded. This is often a scam, and you're a beginning extra, so you want to work on big, well-funded projects anyway.)