I generally start my doctors off young, by using them to heal when they are kids. Usually they'll be an apprentice doctor and become trainess when they turn 14. They'll usually study the plants on their own until they get to adept level, as laurence says; after that they have to be dragged there every time. What with dragging them to the plants and healing the villagers' ailments, most of my doctors make master and several go on to become Elders. It does seem to need some time though. The village needs to be in the late stages (after the puzzles have been completed) as until then they are best used on other tasks, with doctoring just being a sideline.