It depends on the way the casting agency handles their auditions and what the ad agency is looking for. My kids have been asked to do all sorts of things in auditions. I asked my two girls what they've had to do in auditions and here is what they could remember:
They have been asked these questions and more in commercial auditions:
How old are you?
What school do you attend?
What grade are you in?
Do you like school?
What's your friend's name?
What's your favorite (color, ice cream, sport, TV show, subject in school)?
What did you dress up as for Halloween?
What do you want for Christmas?
What did you get for Christmas?
Where's your favorite place to go for vacation?
Do you have any siblings?
Tell me about yourself?
What are your hobbies?
For commercial auditions they have had to study sides anywhere from one line to two pages. However, for a movie audition my oldest has had to learn up to 15 pages (six scenes). Most of the time in a commercial audition they have a few lines or they act out a scene alone or with a group of kids and sometimes rotate rolls with the other kids. They've had to act out a scene with adults - usually an adult(s) plays a parent or parents. They've been asked to cry in a commercial audition. Often they get their picture taken. They have had to play with toys alone and with other kids. They have had to eat something and smile - McDonald's does this sometimes. They have had to pretend to eat something and look sick.
Always have a headshot and resume ready for submission and have them stapled back to back before you get there. I always have a few extra just in case and it has been useful in the past. In L.A. you should make sure you are pre-registered on Casting Frontier and have your bar code with you so you don't have to reprint it - sometimes the line to reprint a barcode can be very long! Always take your barcode with you after the audition to reuse it.
I disagree somewhat with Castlerock that commercials are all about the look. At a young age it is usually about the look but as you get older (pre-teen years) it becomes less and less about the look and starts to be more about the acting. Of course looks matter but it isn't the only thing.
I agree with Castlerock that you should look at the story board. However, they often will ask your child to do something different in the audition. I always remind my kids to simply follow their directions because it may not be like the story board.
Don't forget to have your child practice their slate. Let your child have fun with the slate and show some personality. Remember that a voiceover slate is different than the on-camera slate.
When you sign in always use a pen and put your child's SAG number (if they have one) in the space for the Social Security number - never put your SSN there. By signing in using a pen with accurate arrival and departure times and using your SAG number you ensure your child will get paid when an audition is longer than one hour. I have had casting people try to take away sign up sheets so you can't put your departure time - in fact it just happened last week. They return them very quickly when you suggest that you'll have to let SAG know that they are refusing to allow you to sign out. In California SAG is very good about reviewing these sheets and making sure SAG members get paid. If you are not SAG then I don't think you get paid when an audition runs long.
Of course for other types of auditions they get asked to do other things. For theatre or musicals my oldest has had to learn some dance steps and perform a short routine (and of course sing - from 16 bars up to two full songs). They have had to cry in a movie audition and a theatre audition while performing a scene. They have been asked to cold read a scene or multiple scenes. My oldest has even been asked to cold read an entire play once - they were down to the three finalists and needed to separate them. They have been asked in theatre and movie auditions to read with an accent - American Southern, Scottish or Standard English (also called RP or the Queen's English).
I'm sure others can think of more.
Good luck!