The first step in doing a comparison and contrast paper is to isolate the features of the two stories you wish to compare. Both stories are set in the fictional Yoknapatawpha County, Mississippi, and thus one central part of your paper will be to show what each of the stories contributes to Faulkner's creation of the world and families of Yoknapatawpha. The other major connection between the two stories is the linking character of Colonel Sartoris, a young boy in "Barn Burning" and much older in the context of "A Rose for Emily". Both stories, as with many of Faulkner's other works, show the contrast between the old aristocracy of the south and its traditions and the "new" post-reconstruction south.
You should start your paper with a clear thesis concerning the particular aspects of the story that the rest of the paper will investigate. The rest of your introduction should lay out what sort of supporting evidence for your main thesis will be presented in the rest of the paper .