My 3 year old actively resists 'formal' attempts at learning, any whiff of you trying to get a 'correct' answer out of him he rejects, messes about, obviously began to start getting stressed about getting it so I just backed off.
We read lots, stories and factual books on things he shows an interest in, a lot above his age range, we look things up he wants to know and talk about it. I answer any questions he has as fully as I can and always make time to do so.
His verbal skills and comprehension of ideas are very good, hoping that is the foundation he needs for formal learning and will make it come more easily when he's ready.
We count apples in the supermarket, I've shown him how to sign his artwork with the first letter of his name, I point out letters to him for different things and read signs, and he now starts to ask what letter/sound a word starts with etc, so think they just get there in their own time. If you create the right environment then they will lead it.
I'm definitely concentrating a lot on his confidence, exposing him to new situations, encouraging any interests and an element of risk taking, both physically and with arts/crafts etc.