How do I write a rough draft for a literary analytical essay about the short story "A Rose for Emily" by William Faulkner?

You might begin by identifying a theme of the story, and that theme can go into your thesis statement. For example, Emily Grierson has trouble letting go of the past. When Emily tries to live as though the past were the present, she ends up completely alienating herself from other people and engaging in behaviors that are unsafe and, frankly, gross. In trying to hang on to her beautiful past, Emily Grierson actually becomes something disgusting: she hoards dead bodies and actually looks like a dead body herself. The narrator compares her to someone who has drowned: it is as though she has become pale and bloated after laying in water for a long time.
Her respectability fades when she begins to age and it becomes clear that she will not marry. It fades more when the townspeople identify her house as the source of the terrible smell (that turns out to be Homer Barron's body). It fades even more when she crustily refuses to pay taxes and refers the town's new officials, for proof, to the long-dead sheriff. It nearly disappears, we might imagine, when officials find Homer's dead body in her bed, with her hair on the pillow next to his. Therefore, we can infer that, when someone cannot let go of the past, there is no way for them to have a satisfying or productive present or future.
You might use this theme, or another like it, to form an analytical argument about the story in your thesis statement. Then, each of your body paragraphs can outline one reason that you know this theme to be true, using textual examples.