This quotation is one of Atticus' finest bits of advice to his children in Harper Lee's To Kill a Mockingbird. Scout has had a terrible first day of school with her new teacher, Miss Caroline, and she wants to quit. She knows that Atticus never went to school, and Scout assumes that she will be able to be schooled at home as well. But Atticus lectures her on tolerance, telling her that Miss Caroline had learned a few new things just as Scout had.
"You never really understand a person until you consider things from his point of view--until you climb into his skin and walk around in it."
Scout later applies the advice to her meeting with Boo at the end of the novel, when she stands on Boo's porch looking out over their neighborhood and seeing the past years through his eyes.
The quotation can be found near the end of Chapter 3 (page 30 in my old paperback from 1982; your page number is probably different).