As a number of people have already implied, interactive reading to kids is key (i.e discussing the story as you go along, rather than making them passive listeners). Note however that early reading doesn’t seem to be predictive of superior reading skills at later ages.
Heh, when I was in first grade in one school my teacher had me in the lowest reading class. She had some pet love of the reading groups and lavished all her attention at the top reading group which she would not let me into.
I changed schools, and I had to go to the third grade class down the hall for reading group. 
For background, I’m 60 with no kids and not all that entranced with what they do in general. I have a younger friend, however, who has a 2-year old. We’ve been meeting for lunch about once a month since he was born so I see him growing up. She’s always brought along a picture book of some sort to occupy him during the meal at the restaurant.
It’s been fun since he started talking. He’s been recognizing letters for some time already. I ask him to find certain letters and what letter is that particular one on the sign that’s hanging on the wall or on the menu and he knows.
So if he’s “reading” the word under the picture or he just knows what the object is because he’s looked at it so many times, I don’t know but I’d say he’s well on his way to reading… He’s also to the point where I can have a little conversation with him. I ask him questions and he responds. I tell him something and he makes a relevant comment.
He has exposure to a variety of adults and children his age that are the children of his parents’ friends. They get together regularly.
A bird built a nest near their back door. He got to watch the whole cycle–eggs to the little ones flying away. He sees the flowers grow and the snow fall. His mom listened to classical music before he was born and she continues to mix that up with some kiddie TV shows. A little bit a day.
She’s not trying to make him into anything. She’s just keeping a very curious and active little boy occupied. All of these things, I believe, contribute to the skills he is developing. For me, since I never had my own child, it’s fun to watch him. I love, especially, when the lightbulb goes off and he smiles and laughs because he make a connection he didn’t before.
My mother taught the six of us to read, and she swears it’s physiological–that your brain has to be ready for a certain level of abstraction, and that that point happens at different times for different people. According to her, by 18 months I could recognize all my letters and knew which sounds they made, but I didn’t read until I was 6–just didn’t make the connection. Once I could read, I could read anything. I don’t know why people get obsessed with early reading–everyone knows that walking at 9 months doesn’t mean a child will be a great runner, so why do they thing reading at 3 means you’ll be a genius?