*Disclaimer: my children are probably genetically predisposed to like reading.
Here are all the tips I have to offer:
1) Start early. As previously mentioned, I read to DD while he was still in utero. I didn't have time to dedicate to specifically reading to the unborn when I was pregnant with the other two, but they got much more in utero exposure to books, because I rarely stopped reading to DD. When the babies were born, and really up until the age Gorilla is now, say 10 months or so, they sat willingly for reading, but didn't really seek books out. Keep at it. You might just find them walking and "reading" at the same time, soon.
DD at just shy of one year, with a dumb little Sesame Street book I got at the dollar store. He loved it (I think) because it was tiny enough for him to easily tote about.
Teep at a little over one year, with same dumb Sesame Street book. We got some bang for our (literal!) buck.
2) Make time for it. I was fighting a sinus headache and sore throat over the weekend and complained to my husband that the boys wouldn't stop bringing me books to read. He commented that that was not the kind of thing that would ordinarily bother me. He meant that I pretty much read to my kids anytime they ask. I'm not saying that's what you should do or that anyone else out there has time to do that. My house and my paperwork and my dinner prep have all suffered, but I decided even before I had kids that I wanted my children to love books, and we place a very heavy emphasis on reading in our house.
3) Remain open-minded about the types of books your kids fall in love with. I am (probably obviously) not a huge fan of the book the boys are pictured with, above. But they loved it and I read it. And, in the spirit of confessions, I was never very interested in those books with no real story, pictures of "real" people and things, and some sort of overt educational intent. I got some for cheap or free when I was a bookseller, and guess who fell in love with them?
Matching baby boys looking at boring real people book
Tiny Teep hanging out with photos of real babies
Gorilla having her cake (or well-supervised stolen apple) and reading about it, too
Do I get a little bored with repeating single words while pointing to the accompanying photo? Yes. Do I wish there was an awesome story and beautiful illustrations? Yes. But my kids love these books, and they have learned a lot from them, too! One of DD's first words was "blue", and I remember being so struck by his joy every time he saw something to which it applied - "blue!!" He was clearly thrilled to be able to speak aloud the correct word for a given thing, and it was one of those books (Happy Baby Colors) that provided him with the information about his world. Gorilla is pictured with companion book Happy Baby Words and there's a Happy Baby Animals, too.
4) Don't only read at bedtime. I think a story before bedtime is so sweet. The sleepy heads on my shoulder, the cuddling, and (not least) the favorite books of mine that lend themselves to that time of day. But many people through the years have told me that their kids didn't like reading, and then gone on to say that they only read at bedtime. This is just a theory, but I wonder if reading at a time that many children dread causes an association between distaste for bedtime and distaste for books.
5) If they want to drop it, drop it. A couple of months ago, I started reading The Magician's Nephew to DD. I grew up with the Chronicles of Narnia and C.S. Lewis and have fond, fond memories of read-alouds with my parents. He seemed super interested for the first five chapters, but didn't want me to read anymore on subsequent days. I was a little sad, but thought he might be too young for that kind of book. I put it away and didn't say anything else about it. A few weeks ago, he came to me and asked to read it. He didn't remember the name of the book, but described in detail what had happened up to the point we had read. I got it out and we finished it the next day. As eager as I was to share an experience with him that had meant so much to me, I didn't want to potentially ruin it by pushing it on him.
For what they're worth, those are my tips. My children are still young, and it's possible they'll grow out of their love for books (sad, sad thought!), so I am eager to avoid sounding like a know-it-all. They've worked for us so far, though, and I hope they will help you!
DD in bibliophile's bliss during a bedroom switch