The story can be confusing, yes, because it is told in flashbacks. This is to aid in the effect of the surprise ending.
Miss Emily meets Homer Barron, a Northerner and a blue collar worker who is seen to be "beneath" her, and he "courts" her. Emily doesn't care that the townspeople and her relatives do not approve of the relationship. It is alluded to in the story that Homer Barron is homosexual, as well, so the reader gets the impression that this relationship may not last. Homer sneaks into the back door of her home one evening after her relatives have left and he is never seen again. Because Miss Emily bought arsenic at one point in the story, the reader can assume, once we find out that he is dead, that Miss Emily poisoned him with this arsenic. Hope this helps!