How do auditions for a movie role work?

It all depends. Depends on the role, the director, the type of production. The days of screen tests are most definitely NOT over. All you have to do is go to youtube and type in screen test and you'll see modern actors auditioning on camera. This is what generally happens. When you audition for film or TV, you are sent a piece to learn. It's usually a piece from the script. When you turn up for the test, you fill out your details on a piece of paper...usually it's name, age and agent. if you don't have an agent you write 'freelance'. You stand at a mark in front of the camera and they record you running the scene. Mostly the person reading opposite you is not an actor and they've been reading the same bits over and over, so they're unlikely to give you too much. You may do a couple of takes, you may be asked to do a cold read, they may take a couple of stills - headshot, profile, full-length etc. And that's that. Then you're in the lap of the gods. If you have no acting experience and you believe yourself capable of acting, then learn the piece inside out. Understand the sense of each word you're saying and being said to you. You could try doing some sense memory or practical aesthetics exercises to give you a better understanding. If you don't think you can act...learn the piece inside out as above and then just go in and wing it.

The old days of dong screen tests are gone and won't be coming back. You will just go to some office somewhere and wait for what seems like hours until yo are called in to audition for about a minute.