Have you checked on programs for children at the libraries?
Long before children start to read on their own, they love to listen to stories. Interacting with your child with a good book is a way to instill the love of reading in your child. Even the youngest children benefit from exposure to books and stories.
Holding a book, feeling its texture, learning that we turn pages in a certain way all contribute to reading readiness. The more a parent can do when a child is young, the better ready a child is to start reading on their own when the time is right for that child.
Your library has many books for children, from the youngest to those reading on their own. Library staff will be able to assist you in selecting books of interest to you and your child.
There are many programs for preschoolers now and in the summer libraries concentrate more on programs for school age children. Check back for that schedule.