Walnuts turn ripe during autumn. The maturation process causes the hull to soften and go from a deep green to a yellowish hue. When the hull is soft enough to dent with a finger, it is ready to pick.
When harvesting walnuts, the best practice is to shake the tree and pick up the ones that fall off. Part of the maturation process involves weakening the stem holding the walnut onto the tree. Walnuts generally fall from the tree themselves in the second half of September. It is best to hull ripe walnuts right after picking, as the hull has juice that makes the flavor unpleasant if the nut stays inside too long.