The foundation for learning to read begins way earlier than most people realize. It's not just learning the ABC song, and it's not just learning to recognize letters. It starts way back when you hold your baby on your lap and read the first little board book out loud. Babies learn that books have pages that turn, and pictures that are different on each page, and that when you use this book, you always hear this story, but when you hear that book, you hear that story. Next comes print awareness, knowing that print has meaning, and the same print always has the same meaning. They may recognize the word "McDonald's" even though they don't understand how to sound out the letters.
I think many children can begin to read on their own well before kindergarten. Of course, it's also like learning to ride a bike - for some it just clicks way before others. But there's no need to wait for kindergarten to start teaching your child the basics, just like you don't need to wait 'til the magic age of five, or six to try to teach your child to ride a bike.
One of the best ways (in my phonics-biased opinion) is to get a very simple alphabet book, one that shows just the letter, a picture, and maybe the word. And make sure the word represents the main sound of the letter, not something like "owl" for "O". (My one big complaint about my blue alphabet rugs.) Read the book aloud by saying "A says a like apple. B says b like ball. C says c like cow." Read it over and over and over. I found a great alphabet book like that when Lauren was about 15 months old. She fixated on that book, and I didn't really understand why until I saw her looking at a book (not the alphabet book) and pointing at a word, saying "f". I looked at her book, and sure enough, she was pointing at the letter f. I quizzed her and she knew lots of letters. She knew the whole alphabet by the time she was 17 months old, and I definitely credit that alphabet book. Something just clicked with her, like a child learning to ride a bike at 4. I do believe, though, that kids are capable of getting started way before kindergarten, even before preschool. You are your child's first and best teacher!