I assume that you are talking about what happens in Chapter 11. If that is the case, Atticus greets Mrs. Dubose simply by coming into her house (after knocking and being told to come in) and by going over to where the old lady lay and taking her hand. He does not address Mrs. Dubose by name or anything. In fact, he does not even say hello or good evening -- he just goes over and takes her hand.
Scout is not really sure how the two of them can be so civil to one another. She does not understand how Mrs. Dubose can say horrible things about Atticus and then turn around and be civil to him.
Chapter 11 holds the most evidence to Atticus' attitude toward Mrs. Dubose. This is the chapter when Jem is punished for destroying her flowers. Despite the fact that Mrs. Dubose is cranky, disrespectful, and sometimes downright rude to the children (her disrespect of their father is what causes Jem to flip out and whack all the flowers with Scout's baton) - Atticus always maintains a sense of gentility when talking to as well as about Mrs. Dubose.
When the three of us came by her house, Atticus would sweep off his hat, wave gallantly to her and say, "Good evening Mrs. Dubose! You look like a picture this evening."
Atticus actully does not treat Mrs. Dubose any differently than he would treat any other older woman in the town of Maycomb. He is always a picture of control, politeness and patience. Atticus knows Mrs. Dubose suffers from severe physical pain as well as a morphine addiction. In light of these circumstances, he is able not to let her words affect him as they do the children.