It is not all-boys, obviously. We will be operating under the premise that Watcher's are destined at birth, as Giles said in the first two seasons of BtVS.
They are taught the regular classes- Maths, Biology, Chemistry, Physics, Literature, History, etc., but they also study Demonology, Latin, Sumerian, Greek, Ancient Runes, Mythology, and martial arts. They are taught how to train and prepare slayers, and interact with Slayer school a few times a month.
They are also taught journaling. Every Watcher is required to keep daily diaries chronicling the life of their Slayer, so they are taught to start now.
Upon graduation, each Slayer will be paired up with a single watcher and sent out to their post. So the schools solialize regularly, and the staff observes the students, to see who will be best suited with whom.