Pikachu52
Well-Known Member
My theory has always been that the player carries around a machine that directly downloads the information of the TM into the mind of the Pokemon. That's how I interpreted the TM teaching scenes in Fire Red/Leaf Green. My other thought is that if TMs were to ever appear in the anime, that teaching a TM would require going to a Pokemon Center, where they have these same machines (just not portable).
The Electric Tale of Pikachu had quite a good answer for how TM may work. You open it like a box over the Pokémon's head.