In the book, Davy, whose mother has disappeared, is just about to be hit by his dad with a belt buckle, when he finds himself in the library. He finds out he can jump, and the limits and such and leaves town. He has more and more trouble and when he gets to NYC, he finds out he can't get a job because he doesn't have a GED and can't get a GED without a birth certificate, so he jumps into a bank and carefully steals about a million dollars. He lives on that and meets Millie -- she's about four years older, but they become lovers -- and starts setting up another home near her. He eventually tells her he can jump.
After some sleuthing, he manages to meet his mother, who left because her face was in pieces and her psyche was tattered (both from Dad), and it looks like they'll be good friends. Then an alert comes that a terrorist killed her in a hijacking and Davy starts looking for a way to get that hijacker back.
This is one of my favorite books and I highly recommend it. I'm going to go on to read the sequel, Reflex. The last time I asked Gould about whether there would be another sequel for the books (since the movie is so dramatically different that they asked him to write a book for it (Jumper: Griffin's Story)), he didn't answer.