How did Calpurnia learn how to read in To Kill a Mockingbird?

Calpurnia learned how to read when she was at Finch's landing. A Miss Buford taught her to read using the Bible and a primer.

One Sunday when Atticus is called to Montgomery, the children go to church with Calpurnia. While there they experience what it is like for the poor blacks of Maycomb: The church is without a ceiling and painted walls; pine benches are set out in rows instead of the pews to which the children are familiar. There are no pianos or organs, no church programs, no hymn-books. Zeebo, Calpurnia's son, leads the congregation in the hymns by first reading the line and the others follow, singing the line.

After the service, the children ask Calpurnia about this technique of "lining." Then, Jem remarks that perhaps the congregation could save the collection money for a year and purchase some hymn books. When she hears this, Calpurnia laughs: "Wouldn't do any good...They can't read." Scout and Jem are shocked, but Calpurnia says she is one of only four there who can read."Where'd you go to school, Cal?" asked Jem.

"Nowhere. Let's see now, who taught me my letters? It was Miss Maudie Atkinson's aunt, old Miss Buford--" (Ch.12)

Further, Calpurnia explains that there was no school for the children to attend, so she taught her son Zeebo herself. Scout asks if she taught him "out of a primer, like us?" Calpurnia says that she made Zeebo read a page from the Bible every day, and then read from a book from which Miss Buford taught her.  "...bet you don't know where I got it," she said. The children do not know. Calpurnia said, "Your Granddaddy Finch gave it to me." (Ch. 12)

Calpurnia explains that she grew up between the Buford Place and the Landing. She adds that she worked for both the Finches and the Bufords, and she moved to Maycomb with Atticus and their mother after they married.

This history is not unlike those of others like Calpurnia who grew up on one family's land where they were cared for in other ways than what was necessary for servants. The interest in Calpurnia's education was not uncharacteristic of these families. Later, when Atticus talks to his sister Alexandra, he alludes to the bonds of his and Calpurnia's youth when he says that Calpurnia is a part of his family.