I'm occasionally asked to recommend how an interested child can learn to become a magician. If you've started a youngster with a quality magic set, consider getting them a book to learn from. The cool props that come with a magic set are seductive to most any kid, but how much they enjoy a book on magic will tell you if they're likely to develop a lasting interest.
A good book to start with is Kids Make Magic by Ron Burgess. It's inexpensive, and appropriate for younger kids. In fact, a friend of mine uses it as the "textbook" for the magic classes he teaches for a park district during the summer.
If you know a boy or girl (especially a girl, the world needs more female magicians) that really shows some spark, then it's a good idea to pursue a magic class or personal instruction. Many local community education groups will offer magic classes during the summer, or check at your local magic shop (look in the phone book under "magician's supplies") for a referral.