My son is three and a half. He enjoys sharing that activity with me and often asks for the board and stones. He's full of interest for the game. He can also be quite focused when playing any game, but he prefers making up his own rules. He has objections to following other people's rules
Go is one of the activities that make him work on that. Our material:
- Indestructible cheap plastic stones and indestructible cheap board
- Computer and android tablet for various go software
What he already learned:
- How to store white and black stones in separate bowls (and not eat them, mix them, throw them, other parents will complete for me this non-exhaustive list...)
- How to put down the stones on the board, on the intersections, not in the squares
- Players take either white or black and play alternatively
What he's currently learning:
- How to capture a single stone
- Not move stones around after they were put on the board
- Not remove stones after they were put on the board, unless captured
Point one is the main focus. The rest will make more sense for him when we start playing capture go together, so I'm not particularly strict on enforcing it for now.
If there's a book in my hands, he'll grab it. But he's young, so maybe that's just normal for his age 
Even my husband agrees to play me on that one. If I'd known that, I would have bought it much earlier!