Let the child have some board books of his own to hold. Sandra Boynton's MOO BAA LA LA LA and books by Tana Hoban and Helen Oxenbury. The child from one to two should have a variety of books. Books should be short, colorful and without unnecessary detail. Continue nursery rhymes.
Manipulative books are very popular.
The child from two to three is ready for more complicated stories and pictures. Books that are cumulative or repetitious are big hits. Children of this age like to think they are independent yet cared for. ARE by Maurice Sendak are perfect now. Seek out books with imaginative use of language.