This line is one of the most important quotations in Harper Lee's novel, To Kill a Mockingbird. Atticus delivers this bit of superlative advice to Scout after her terrible first day at school. Scout has had to deal with her raw new teacher, Miss Caroline and her ridiculous demands; she has fought with Walter Cunningham Jr.; she is then scolded by Calpurnia after her inadvertent insult to lunch guest, Walter. When she tells Atticus that she would prefer not to go back to school again, he tells her
"... that if you can learn a simple trick, Scout, you'll get along a lot better with all kinds of folks."
Atticus's statement is simple. By putting yourself in another's place and trying to understand their way of thinking, you will better be able to deal with multiple points of view. Both Jem and Scout take the advice and use it later in the story.
This is plain as day. Atticus has wanted his children to look at life from Boo's perspective, from a Negro's perspective, and from their peers perspectives throughout this story.
What may be confusing here is the idea of climbing around in someone's skin. I think it would be easy to just put someone's shoes on. You would feel that the shoes were a little tight or a little loose. And you then could give the shoes back.
To walk around in someone's skin would mean adopting their life characteristics, the things they are persecuted about, praised for, expected of, and stuck with. You can't just quickly adopt someone's life traits. This would take deep analysis and consideration. Scout only ever gets this when she stands on Boo Radley's porch and imagines what it might have been like to watch her over the years.
You cant make a prejudice judgment on someone without knowing the facts.