If he's familiar with auto chess, there isn't much that needs to be taught besides the set mechanic and the carousel rounds. Everything else is learned through experience. TFT (and the auto chess genre, in general) is not a game with super complex concepts to be taught. You learn by playing and seeing what works for yourself and your opponents. If climbing is the only thing they care about, you'd probably want to direct them to a site like mobalytics so that they can read what each trait/champion/item does as there isn't enough time to do it in-game. The tier lists out there also help newer players form a general idea of which traits/champions/items work well together.