It is in Chapter 7 of Kate DiCamillo's Because of Winn-Dixie that Miss Franny Block explains how she came to own the library and be its librarian.
According to her story, she lived in Florida as a young girl, when Florida was still very rough and wild. In this rough wilderness, when Miss Franny was about the same age as Opal, which is ten years old, Herman W. Block, her father, said she "could have anything [she] wanted for [her] birthday." He was able to get her anything she wanted because he was very wealthy. Miss Franny further explains that she loved to read, even as a little girl, so she told her father the following:
Daddy, I would most certainly love to have a library for my birthday, a small little library would be wonderful. (Ch. 7)
So, he set to work building a small house and filling it with books, and when she was only Opal's age, Miss Franny became the librarian of that library her father had given her and has been ever since.
Miss Franny tells Opal the story of how she came to be a ten-year-old librarian the same day she sees Winn-Dixie looking in through the window, standing on his hind legs, and mistakes him for a bear she once saw in the library when she was a girl. Opal brings Winn-Dixie inside the library to hear the story too. After telling the story, Miss Franny confesses to how lonely she is since all the people she knew back when she was a girl and growing up are now dead. Opal suggests that the three of them--Opal, Miss Franny, and Winn-Dixie--all be friends. Miss Franny is so impressed by Winn-Dixie's politeness, friendliness, and smiles that she not only agrees to friendship but permits him to come into the library any time he wishes.