As soon as they could hold one. In our case, about 5 or 6 years old. Daisy "Buck" BB gun, safety glasses, pop can at close range on the grass, nothing hard within 100 yards past it. ( I had to #### it) At that age, there is lots of curiosity, but it often only takes 2-3 shots to satisfy it. lol My kids are 11/14/17 now and the two older ones still shoot with me sometimes, and I don't think the 17 year old knows how to miss hand-thrown clays with a 12ga. My 14 year old has her FSC/Hunter's safety course and holds a hunter's apprentice license. Proud dad.
Hint: balloons pinned to the ground with a stick make pretty exciting targets for kids. I used to keep a couple of bags of dollar-store balloons in my ammo box for that purpose alone.