The best time to introduce books and reading is when they are infants and still in their crib.
Don't wait until they go to kindergarten.
When our first child was born, my husband brought in a little book and started to read to her when she was only a day old! We both continued to read to her until we could read books together and then eventually I had her read to me.
The benefits of books are:

• Books give your baby visual stimulation
• Books promote language skills by listening to our language and by hearing correct speech
• Books can be comforting when they hear your soothing voice or excitement from dramatic words
• Books encourage exploration especially the touch-n-feel and lift-the-flap books.
  

With my daughters, they would love to read the same books over and over.
I would keep reading them the same books, even though I was tired of them! They loved it and they loved being able to see and remember something that they have seen before.
My daughter would sit on the couch with a huge pile of books.
She would turn all the pages and babble right along (we couldn't understand a thing she was saying!).
She was so proud that she was reading all by herself! Read to your baby every day, either before bedtime or before nap time, or both.
Show your baby that story time is special and that you want to share that special time with her (him).
The following is a list of our favorite books:

• Good Night Moon by Margaret Wise Brown
• The Very Hungry Caterpillar by Eric Carle
• The Tale of Peter Rabbit by Beatrix Potter
• Rainbow Fish by Marcus Pfister
• Sheep in a Jeep by Nancy Shaw
• Barnyard Dance by Sandra Boynton
• The Going To Bed Book by Sandra Boynton
• When Mama Comes Home Tonight by Eileen Spinelli and Jane Dyer

There are thousands of children's books available that are also very good.
These books were special enough for me to remember them after several years.