Lee begins characterizing Mrs. Dubose directly. She is described by Scout as "the meanest old woman who ever lived." But she quickly moves to more indirect characterization as Scout (as the narrator) describes the way that Mrs. Dubose would interrogate Scout and Jem about their behavior and constantly give them a dour look, apparently judging them harshly, even going so far as to criticize Atticus for "letting his children run wild," a cardinal sin in Scout's book. She ruthlessly insults the children and uses their love of Atticus against them as she includes him in her rantings.
But Harper Lee likely characterized her up this way in order to allow the reader to share in Jem and Scout's distaste for the old woman. Because once they are sentenced to read to her after Jem's attack on her camellia bushes, they learn that something is wrong with her but they don't know quite what.
And the last part of her characterization is direct as Atticus explains to the children that she was addicted to morphine and he also outlines how hard she fought against the addiction and that "she was the bravest person [he] ever knew."