You’ll need a guitar, tuner, strap, case, and picks.
Depending on your kid’s age and size, a ½ or 3/4-size guitar is usually appropriate. For our lessons, an acoustic guitar is better than a classical. (If you’d like your child to learn classical guitar, I can refer you to some other great teachers.) It’s okay if the guitar has nylon strings, but steel strings are better in the long run. If the strings haven’t been changed in a while, we recommend changing them.
We recommend the Snark, but any chromatic tuner will do.
If you’re not sure what kind to get, bring the guitar with you to a guitar store like Guitar Center.
Especially if you spent good money on a guitar, you’ll want to protect it when transporting to and from lessons.
I supply students with a pick, but they inevitably lose them again and again. Picks are pretty cheap and they’re fun to collect, so get a handful.