Learning two or three champions in each role is a good way to make you aware of what each role does, variations included, which should help you be a better strategist and learn to make better team compositions. Learning to play a bunch of different champions in this way should also develop your mechanical and tactical skills by teaching you how to respond to different situations and champion kits. I think learning several champions in each role is an important step toward being a better player, but as a teacher-to-be, you should know that you'll need to do more to learn the game. I recommend that you spend some time trying to learn general game strategy. Study guides, watch shoutcasted professional games, spectate high-level ranked games, watch youtube videos, and read up on the excellent posts made in the Tips & Tricks board (I am particularly fond of this post). Pay special attention to wave management (freezing, pushing/letting push, setting up large waves for split lane pressure), effective warding patterns (every player should buy wards and upgrade their trinket), rotation between objectives, and the advantages of split-pushing versus team fighting. Once you are comfortable with this knowledge, try to guide your teammates to employ it in a friendly, constructive manner. Note that kills at high level play almost always have a specific objective in mind, and that they rarely chase enemies into unwarded territory.
The most important part is, of course, the will to learn. After each game finished, play made, or death inflicted, try to take a moment and think about what you could have done better and what other players did well, then try to implement those changes one at a time.
Have fun, good luck, and happy farming!
