Near the end of chapter 3, Atticus says to the children that he never went to school. He's discussing their situation with Miss Caroline. He doesn't want Scout to upset her teacher by continuing to read at home, so he tells Scout to keep between the two of them.
Atticus and his brother must have learned to read and write, like most of his generation at home, because both of them were able to go on to college to pursue their careers. Atticus was admitted to the bar, and his brother Jack went on to study medicine. So both were taught pretty well before going off to college.