I like to read and I'm always a bit surprised when people say that they don't like to read. On the other hand I totally understand, especially when I think about my experience in high school English class. I already liked reading by the time that I reached High School, but if I hadn't I honestly think that it might have convinced me that I didn't like to read.
High School for me was quite a while ago and perhaps it has changed, but there are a few ideas that I still see from time to time. The first of these is that we all need to stop looking down on books. I don't care whether it's Twilight, Harry Potter, Fifty Shades of Grey or the most recent Stephen King novel they are popular for a reason. Some of those are clearly not written for me and if I read them I'd either be annoyed or bored. On the other hand I know plenty of people who would find the Martian Chronicles, The Foundation Trilogy, 1984 and Ender's Game boring. I can even imagine a person who wouldn't enjoy the Hitchhiker's Guide to the Galaxy. (Though I'm not sure I can explain that.)
All of these have something in common with every other book that has ever been written. They are finite in length and they were influenced by other books. Did you like the Twilight books because of the romance, perhaps you should try a Jane Austin novel. Were you intrigued by the vampires, Bram Stoker's Dracula is considerably more interesting than you might think (And Mina Harker is a way more interesting female character than any in Twilight though that's just my opinion.) Know a kid who has read Harry Potter 4 times, ask some questions and find out which of the many great books fit what they liked. Whether it is The Hobbit, The Once and Future King, The Dresden files, The Hunger games or any of a dozen other ideas you have one huge advantage. They are already interested in reading. You just have to find books that meet them where they are at.
And that's the problem I had in my High School English class. I had an excellent teacher, a good school and I was interested in the subject but I had no connection to Shakespeare, Beowulf or most of the other required reading. And while I completely understand the desire to get people to read important books, those books are important because they connected to the people at the time. Shakespeare is still remembered because he made plays that people wanted to watch, Beowulf was a popular story and the Canterbury Tales has significant amounts of toilet humor.
Here is the secret, if you want kids, or adults, to read you have to understand why people read. People read because they enjoy it. People read because they form connections to books, because a book, better than any other type of media can grab you and say that someone else understands how you feel, that there are people that feel the same way. Remember that confusion and anger in high school, so does Holden Caulfield. Do you feel the weight of the world on you, like everyone is counting on you. Harry Potter certainly understands that. Are you exhausted and just want to give up. Sam and Frodo certainly could relate. I don't know perhaps if you're a teenage girl trying to deal with romance Bella might actually make you feel better. The point is if you are going through anything there is a book character that can step up beside you and say, "I understand and other people go through this too." And while that may not solve the problem it certainly helps. But it requires the right book at the right time, not just the important book.
I believe that if you can get the right book into the hands of anyone and get them to read enough to understand that it is speaking to them that they will enjoy it and even if they don't make the time to read more books they are going to at least understand the value and perhaps the next time they need a book they will seek it out but at least they might have some positive memories of that book.