How does the black community show appreciation to Atticus?
They do this in two ways. First, all of the black people who are sitting in the balcony stand up as Atticus is leaving the courtroom. It's a particularly moving scene in the movie, as the lower courtroom is empty, and the balcony is completely full of black people, just standing in silence as Atticus walks out.
The other thing they do is send over a lot of food to the Finch house. Atticus mentions something about dinner or food to Calpurnia, and she responds that they have more than enough food--the black community has been sending it to him to thank him for what he did. Atticus, being the honorable man he is, insists it's not necessary.