The short answer to that question is that nobody knows who the narrator is. Or you could say that the only person who truly knows the narrator's identity is William Faulkner himself.
The narrator remains unnamed for the entire story. The narrator uses the collective pronoun "we" in reference to himself or herself. It's not even known if the narrator is male or female. "We" allows the narrator at times to be the collective voice of the town itself or the townspeople as a whole. Critics also disagree on who exactly the narrator is. Some say that he/she is a former lover of Emily's or even the town gossip. There is some speculation that the narrator is Emily's servent -- Tobe. This suggestion has some merit, because the narrator has a fairly intimate knowledge of Emily. At times, the narrator refers to Emily as "Miss Emily," which sounds like the language a servant might use.
At one point near the end of the story, the narrator switches over to the pronoun "they." It's only briefly and very subtle, but it functions as a way to distance the narrator from the townsfolk. The reader is meant to interpret this as a sign that whoever the narrator is, it is someone that cared for Emily more than a common townsperson.