At a casting for print usually your photo is taken - and usually the person taking the photo is the photographer who is hired for the job or the casting director- you will sometimes hold a piece of paper that has your name on it. Or you will be given a number. Like # 15. And you will hold up the card, or paper with the number on it, and then you will also have another piece of paper with all your info on it. Such as: Your name, height, weight, measurements, sizes, and your agency name and number or your own phone number.
For an on camera modeling job for a commercial or film, you will have to slate your name on camera and usually the camera will want to pick up your full body and profile.
For an acting audition or speaking role there will be "side" given, which is a sample of the script you will read. You could read it infront of a camera as well, which the casting directors will keep and review later.
At some modeling castings I have had to act too such as pretending to catch water in my hands at a hand casting, or hand off a beverage or pretend to apply cream to my face, or even brush my teeth...sometimes at the casting you have to show the casting director how you would look portraying the job before you even book it. Your photo is usually taken by yourself, straight on, like a headshot, sometimes the casting director asks you to smile, sometimes just a plain face, sometimes jumping or giving a side profile. Other times you could be posing with other models/actors at the casting if it is for a job that requires more than one model- the casting director might want to see how you look with other models, and how natural you look. This comes into plays when "families" or "couples" are being casted and they need to find people who look similar and look good together.
For runway or fashion shows, they measure you, you will be fitted in the clothing to see if they fit, how they fit and how you look walking in them.
Bring photos of yourself or your own compcard. Which you will leave with the casting director, photo editor, or photographer sometimes as well. Put your agency phone number on your card, or sometimes the agencies give you stickers with their contact info on it so you can put one on your compcard.
Usually it can take anywhere from one day to a week to hear back about the job, so don't dwell on the casting, continue to strive and pursue more modeling work. Staying busy and continue to be ambitious is best while you wait to hear from a job, because it is a very competitive world.