I prepare a special stew that makes the other villagers sick and then I use the trainee doctor (or children) to cure them, and then they improve in the skill. And I make all the villagers eat from the stew until is gone, and then the doctors go on their own to cure the people.
And I take the doctors to study all the flowers around the island. And just let them be... but if you start when they are children, by the age 30 they'll be master doctors.