You're correct to assume that Atticus had no formal schooling when he was a young boy (although he did go to law school as a young adult). In Chapter 3, Scout complains about her terrible first day of school and tells Atticus,
You never went to school and you do all right, so I'll just stay home too. You can teach me like Granddaddy taught you 'n' Uncle Jack.
It wasn't uncommon for children to receive their educations at home--from their parents--during the time period in which Atticus would have been a boy (the late 1800s). However, Atticus reminds Scout that laws have changed--and that he would end up in jail if he failed to send Scout to school.