I've been thinking a lot about how my boys got into reading (especially now that I know their friends don't read!). This approach won't work for everyone, but it's how we got to a place where both boys are avid readers.
First, I read A LOT, and my kids see me read. When they were very young, after reading them a quick bedtime story I'd pick up my own book (l love the Kindle Paperwhite for letting me read in the darkness of my kids' rooms!) and sit while they fell asleep. It was also great down time for me after along day at the office.
Second, when they were in early grade school (first through third grades), I relied a lot on their teachers for book recommendations. There's wonderful middle grade books out there that I wouldn't read myself, so I had to trust others to judge what they would like. Also, I never said no to an age-appropriate book no matter how much I want to wrinkle my nose: when they wanted to read Captain Underpants and Fly Guy, I supported that. And I've said before, Diary of a Wimpy Kid was like a gateway drug for reading!
Third, once they were a little older (upper elementary, grades 4-5), I started reading books I thought they would like. The books are quick easy reads, and the time was well spent--when my kids read something I'd "pre-screened" we could talk about the book. Fun times.
Now my oldest is reading at adult level, but also quality YA titles. We often read books at the same time, and I recommend books that were my favorites when I was a teen. He's started on Stephen King, and says his favorite book of all time is 11/22/63.