On your body: Clothing will depend on the season. Layering is generally recommended, especially in fall and spring, when it could be chilly when setting up and standing around waiting for your turn (during group lessons). Close-fitting tops and bottoms are best, to minimize any bunching when you put on the harness provided by your instructor.
On your head: Helmets are recommended and probably required, depending on your location. Make sure they’re a part of your lessons package; if not, rent one separately.
On your feet: This will depend where you are. For dune lessons, like those given at Kitty Hawk Kites in Kitty Hawk, N.C., you can be barefoot or wear socks for minimal protection. On rockier terrain, light hikers or trail shoes are probably fine. Sneakers will work for grassy venues.