I'd say when they show an interest. Bought my son a little plastic toy bow and "nerf" arrows when he was about two, after he kept trying to shoot my bow with me. He shot it until he broke it (a week or two), but it proved to me he really had an interest and could do it.
Got him a tiny selfbow and tiny aluminum arrows, and he's been at it ever since--he's 12 now, and his "collection" consists of that first selfbow, a laminated longbow, and two take-down recurves.
He's had ups and downs--braces, glasses, and some major growing spurts all affected his shooting. He's getting it back now, after the last growing spurt and getting his braces taken off. Last Saturday we shot at Lost Tribe in TN, and he had the second highest score of everyone there (one guy beat him by one point). He shot a 225 out of a possible 260 (26 targets, 0-5-8-10 scoring).
I agree that it's important to keep it safe, keep it fun, and keep a bow they can shoot comfortably. They will shoot better and be able to shoot more, and they will enjoy it more that way.
Chad