Jem and Scout certainly learn a lot during the course of To Kill A Mockingbird, and their "education" comes from experiences and interactions with many different characters.
Primarily, Scout and Jem learn what's important (and what really isn't) from their father. In Chapter 10, Scout complains that her father is old, works in an office (as opposed to working on a farm, working as a truck driver or a sheriff, or working in a garage), and has bad eyesight:
He did not do the things our schoolmates' fathers did: he never went hunting, he did not play poker or fish or drink or smoke. He sat in the living-room and read.
From this description, it's safe for readers to assume that Scout is too young to appreciate that her father's work (and beliefs, and attitudes) is very important. As the novel goes on, though, Scout and Jem observe Atticus as he defends Tom Robinson; he is ridiculed by Maycomb's citizens, yet he doesn't let this ridicule stop him from doing what is right. Atticus teaches the children not to judge people until you consider things from their point of view--a lesson that is too difficult for Scout to understand at the beginning of the novel. Ultimately, though, Scout and Jem learn that their father is a good man--and that is what is most important.
This idea is further reinforced by Miss Maudie, the Finches' neighbor, who doesn't fall victim to the same prejudicial thinking that plagues most of Maycomb's citizens. Miss Maudie tells the kids that their father does a job that most people couldn't handle, and she echoes Atticus's instructions that the children should not judge people before they know them.
Finally, through their interactions with Boo Radley and their indirect involvement in the Tom Robinson trial, the children learn that it is unfair to judge a person because of his skin color, because of rumors about him, or because of any other information they get second-hand. By the end of the novel, Scout and Jem learn that
You can't really understand a person until you consider things from his point of view--until you climb into his skin and walk around in it.
This advice, offered by Atticus at the beginning of the novel, finally resonates with Scout once she has seen the injustice done to the Robinson family and to Boo Radley.