Atticus lets his kids make mistakes. This is one of his methods for teaching them and making sure that they learn for themselves. In this vein, he also emphasizes the idea that the kids have power over themselves and their own choices. This creates responsibility, in expectation and the kids' psychology.
What today's society refers to as "character education" is probably the greatest education Atticus gave to his children. In fact the title of the book is from one of his own lessons "it's a sin to kill a mockingbird." However, Atticus's lessons weren't didactic--don't run with scissors, look both ways before crossing the street. Atticus wrapped the lessons in love, common sense, goodness, and then let the children discover the truth of the lessons in their own experiences.
Atticus teaches his children the cardinal virtues; above all he teaches them that "Pride goeth before fall." His quiet example, demonstrates to them that people will know what they are by their actions. For, what they say will matter not if they do not act upon their beliefs. Atticus Finch practices all the ethical behavior and morals that he teaches and the people of Maycomb, aware of his integrity, give him great respect, as do his children.
Atticus teaches by example. He plays down the "self" and focuses on the greater good. For example, he never tells his children he was a great shot in his youth because why would it matter? But when the rabid dog is in the street he puts those skills to use because it is for the safety of the children and the neighborhood. We surmise that Atticus is the best lawyer in the area, but Attitus never brags about how many cases he has won or lost, he just gives the most vigorous defence for Tom Robinson that he can. When he loses, he doesn't point fingers and place blame, he actually acknowledges how the mere time spent on the deliberation is a remarkable change from the old status quo. He teaches his children to be humble and to do the right thing for the right reasons.
I agree with the first post in that I think that the most important education that Atticus gives his children is the "life lessons," not academics. Atticus is teaching the children how to be good people, not how to be smart. So he gives them lessons by telling and showing them how to treat people like the Cunninghams and Miss DuBose. He gives them life experiences by having them attend the black church. He counteracts Aunt Alexandra's push to make the kids feel superior. In these ways, he is giving them a very important education in how to be good people.
Although Atticus never went to school himself, he wanted to make sure his children received a good education--both in and out of the classroom. He had already taught Scout to read before she entered the first grade--unusual at the time and even today. Calpurnia had taught her how to write cursive--unique for the first grade classroom. Atticus teaches by example--he spends a great deal of each evening reading--and he reads with Scout each night. Scout tells the reader that reading is also a priority with Jem. When Scout wants to quit school, pointing out that Atticus didn't go, he comes up with a compromise: They will disobey Miss Caroline's demand for him to stop teaching her if Scout will continue going to school. But Atticus stresses more than just academics. He wants his children to treat people with respect and come to him when they have problems. Despite his busy law practice, he always has time to talk with them and explain any questions they may pose. He tells it to them straight because he knows that children can sense "evasion quicker than adults, and evasion simply muddles 'em." Atticus' ways worked with his children, as we find out on the very first page of the novel. Even as adults, when Jem and Scout had an argument, "we consulted Atticus."