We know that Romeo could read and write. In the second scene of the play, when the illiterate Capulet servant approaches with the guest list to the party, he asks if Romeo can read:
PETER: Perhaps you have learned it without book. But I pray, can you read anything you see?
Romeo is a bit demeaning when he says:
ROMEO: Ay, if I know the letters and the language.
Though he is intending to be flippant (a result of his attitude over Rosaline), here Romeo suggests that he has been formally educated in reading and writing, and perhaps knows more than one language.
It is likely, then, that both Romeo and Juliet were formally schooled in the basic subjects of reading, writing, and mathematics. In addition, they are likely also privately tutored in the arts, things like painting or singing, as well as fencing, dancing and etiquette.
The formal and personal education the two likely received would also contribute to the idea that both Romeo and Juliet were sheltered and spoiled. This helps to explain their lack of sound judgement in matters of love and relationships, as well as their hasty decisions leading them to getting what they think they want immediately.
As far as history is concerned, they would have tutors teaching them all the stuff of back then. You know, how the world is flat and travels on a turtles back. that kinda stuff. ^-^ But in the play, Shakespeare never mentioned schooling.