Hi. Can't help you with agencies, but can help you with the - how does it work -
You will register with an agency. From there, they will call you if and when a casting agency need kids which match your child's age and sometimes look. Sometimes the requirements are very specifi, blue eyes, blonde hair etc. and you will waste your time by taking your child (and yes some agencies will still try and send you - very annoying so you need to find out what the script is looking for).
From there you will take your child to the casting - they will always only call you a day in advance and sometimes the same day - so you need to be able to get away from work if you work.
Sometimes you will be lucky and it will be quick. You child will get a number and then get called in and asked a couple of questions and sometimes they ask them to do something. You are not allowed to go in with them, only if they are very small. Sometimes there will be like 100 kids at the same time and it can take a couple of hours.
Then you go home and if you child is selected, they will call you and you need to take her back once again. They call let's say 10 - 20 kids back that's been shortlisted. From these kids they will choose the final kid(s).
After this you will need to take your child for a wardrobe fit - they will tell you where and when. This can take anything from 10 minutes to 4 hours.
Then on the shoot day(s) - you need to be there normally from quite early - about 7 or say and you will stay most of the stay. Your child is only allowed to work a certain number of hours per day, but this is broken up so you will most probably be on set for the entire day. One parent is normally allowed to stay on set with the child, but once your child reach school going age, no parents are allowed on site.
And that's about it. Hope it helps.