Anyone can teach a class, there's no real way to do it. You don't really need to be technical. Just explain what you need to do and show the kiddies how to do it. There can also be more than one teacher per class, but I'd say two should be the limit.

List of Availible Classes:

Ninjutsu- taught by Raidou Kuzunoha
Taijutsu-
Genjutsu- taught by Ryusei Shiroya
Tracking and Survival- taught by Ren Yosoke and Testu Yosoke
Kunoichi Training- taught by Ren Yosoke
Swordfighting- taught by Tetsu Yosoke
The Art of Summoning- taught by Asano Kamataichi and Ryo Aiko
Projectile Weapons-taught by Sinthiss Vaan
Puppeteering- taught by Kaano Raeunin