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The first example is when Atticus asks Scout to step into Miss Caroline's skin and understand that it was her first day of school too. He asks Scout to see things from Miss Caroline's perspective as a new teacher in a new town.
Another example is when Atticus asks the children to step into Boo Radley's skin when they are trying to get him to come out to play. Atticus tries to get them to understand that Boo might not want to come out. When Tom Robinson is convicted, Jem begins to understand and empathize with Boo Radley even more as he becomes aware of the prejudice in the town. He sees that Boo is staying inside to avoid that prejudice.
A third example is when Atticus tries to get Jem to understand Bob Ewell's anger after the trial. Atticus explains that from Bob's perspective, Atticus made him look like a fool on the witness stand and Bob's anger is a natural reaction to his feelings of humiliation.