What happens and what can be done on a petty larceny charge for a minor?

Depends on the community, the value of the items taken, and in no small part, the attitude of the minor and parent when they meet with the prosecuting authority. You can discuss specifics with counsel of your choosing if you prefer to have counsel on board. Most attorneys who regularly practice in the jurisdiction you are dealing with will gladly have a no obligation consultation with you on the local practices in their communities.