Once Harry was healed the 6 started teaching him many things that would be useful in his time. Like the languages of other races of the magical world; Murmish, Chentarian, Elf, Goblin, and many more. He also was taught to speak in the other human languages: French, Italian, Indian, Spanish, Latin and many more. Harry could even speak to animals, snakes and owls being the easiest of them all.
Once he was 6yrs Harry started to learn potions, herbology, fighting: sword, hand-to-hand, bow/arrow, and knives, as well as non wand related classes. But learning how to make wands, staffs, brooms, even rooms at the castle, was his favorite activity.
Now at 7yrs of age and having made two fully functioning wands one he uses, Harry starts to learn charms, transfiguration, curses :in the old days they were taught: and how to duel. By the time Harry was 9yrs he was ready to head back to his time asking to have forgotten most of the things till he magically was considered an adult.