The age limit for most general interest shows is 18. Shows targeted for children may have age limits from 10 to 16. It is rare to find shows that allow audiences under 10 (even 10 is rare), but it occasionally happens. There are far fewer opportunities to be in a children's show audience, because there are fewer live shows for children.
Most kid's shows that require an audience are either Nickelodeon shows, Disney sitcoms or game shows. You used to have to go directly through Nickelodeon for their tickets, but they are now listed on Audiences Unlimited at www.tvtickets.com. They also have tickets for several children's sitcoms. Additional youth-oriented reality shows are listed on www.ocatv.com.
Attending a TV show taping requires a certain amount of patience and self-restraint, which is why the minimum audience age may be higher than the target viewer age for a particular show.
See Audience Etiquette for more tips.