Nick Studios is a fun thing to do; be aware, however, that it is time consuming if you are on a limited schedule.
Here's the basic procedure as of November, 2000. Tickets are distributed on a first come, first serve basis the day of the show. Most people line up about 2 hours prior to this - for us we got on line at 12:00 for a 2pm ticket distribution. Everyone in your party MUST be present to receive a ticket - you can just let one person stand in line UNTIL they begin distributing tickets but everyone who wants a ticket must be there when the distribution begins. For Slime Time in November, there were 3 callback times starting about 3pm. If the show is outside, there are a pretty good amount of tickets available. If the show is inside, however, there is limited seating. Inside shooting does not only occur because of bad weather - and no one seems to know if the shooting is inside or outside - so your wait may be in vain. Once you receive your tickets, line up for the show about 45 minutes before your ticket time. This will give you a chance to see the previous segment and maybe be on a live commercial for Slime Time.
My understanding is that contestants to appear on the show are chosen in advance in the park at random. If your child is lucky (and mine was), they do spur of the moment pies in the face. This child will be chosen from the children on the show. It was an experience he will never forget.
Also, don't wear anything with logos or advertisements on it. You will be asked to turn clothing inside out, take it off or wear it backwards. The only ads allowed are for Nick.
This process pretty much took up half a day at US. It worked for us because we were burnt out from amusement parks in general. It was fun, exciting but also involved alot of waiting around.
Hope this info helps you.