To play in a rated tournaments (almost all non-novice tournaments), your child has to be an USCF member.

The annual membership is much cheaper than any other cost related to your child's chess activities, even less than registration fee of one tournament, or tuition of one chess lesson. Therefore there is no reason not to sign up for a membership if your child wants to play serious games in tournaments.

At most clubs, you can sign up membership on the spot. They have signup form and will collect the membership fee for USCF. But it's also easy to do it by yourself in 5 minutes. You may want to sign up online by yourself, use the website:

Use this site when searching for tournaments and checking your child's rating.
Load the uschess.org page:

us chess federation
  • on the upper-right corner, find "Join/Renew"
  • use the third option "If you have problems or if you you want to skip the questions and go straight to the membership webstore, click here.", which is much easier to navigate
  • you will see a table with the list of membership type
  • select the one you want and 
  • fill in other information

Your child will become a member right away. S/he will receive a membership card in a few weeks.