As with every other important lesson Atticus Finch teaches his children, what he teaches about understanding is illustrated through his best method, which is shown by example. Atticus teaches them to treat everyone with respect. When passing Mrs. Dubose's house, for example, he tips his hat and says, "Good evening Mrs. Dubose! You look like a picture this evening."
Also, as with his lesson with Scout on the first day of school, he teaches his children to try to understand things from other people's points-of-view. In particular, with Mrs. Dubose, he teaches Jem that her battle with a morphine addiction is the driving force behind her actions and attitude. Once Jem undeerstands this, while reading to her every day, he is able to be unaffected by her antagonizing and belittling language.
By remaining emotionally uninvolved with the petty insults that come at him from people in town, Atticus teaches his children that the best way to deal with antagonizing and belittleing language is to respect themselves first and to treat everyone with the same kind of respect.
Atticus Finch teaches his children tolerance by practicing it himself.
Having known Mrs. Dubose for years, Atticus must recognize her normal behavior. So, when she insults him or the children, Atticus simply reacts with politeness and tolerance because he knows the underlying cause.
After Mrs. Duboses's remarks become caustic when the children pass by her house on their way to meet Atticus coming from his office at the end of the day, Jem decrees that he and Scout must run swiftly from the post office corner in order to avoid having insults hurled at them. However, as the children and Atticus near the Dubose house on their return home, their father stops and waves gallantly to Mrs. Dubose and says,
"Good evening Mrs. Dubose! You look like a picture this evening."
The patient and charitable Atticus then tells the elderly woman the courthouse news, and he expresses his hope that she have a good evening. In awe after Atticus exhibits this charitable behavior, Scout thinks that Atticus is "the bravest man who ever lived."