This is a fairly big question -- broadly considered, diction means word choice, and author's obviously choose thousands of words when they write stories. What you are actually being asked to consider, I think, is to give examples of specific diction that enhance the meaning of the story or contribute to the overall effect of the story. By considering it this way, you have a more focused purpose to your analysis.
With that in mind, you should think about what this story is about or what it means. It is a story of a young man who is tempted to a meeting of witches being held in the dark forest. He leaves his wife and takes this journey with much trepidation, and in the final moment of the meeting decides to turn away from the devil's promises and return to town. Unfortunately, the experience leaves him embittered and cynical.
Here are a couple of examples of diction that contribute to the overall meaning of the story. One of the most obvious choices made by Hawthorne is in his naming Brown's wife, Faith. There is an obvious pun here -- faith as in faith in God, and faith as a name with virtuous connotation. Each time Brown mentions his wife by name he is also referring to his religious faith. He tells the old man at the start of the story that he is late because "Faith held me back awhile." He literally means that his wife wanted him to stay for a few extra minutes, but he also implies that his faith and his not wanting to be sinful kept him from this potentially evil trip he is on.
With the description of the witch meeting the narrator says that Brown felt a "loathful brotherhood" with the others assembled. Loathing is a extremely loaded word implying extreme disgust, but it becomes almost oxymoronic when paired with brotherhood which connotes a closeness and indivisible bond.
The fire imagery and language throughout the meeting also connotes the fearsome and hell-like atmosphere that Hawthorne is trying to create. There were "four blazing pines that through up a loftier flame," a "blazing rock," a "canopy of fire" and most frightening, "flashing forth...in a sheet of flame, the fiend." All of these words suggest fire, heat and a stereotypical image of hell. Hawthorne even mentions the "hell-kindled torches" held before Faith. The collective connotative power of these words and descriptions serve to make this meeting a frightful and evil gathering.
If you read and consider the story carefully, you will find that many many words are interesting or powerful in how they add to the meaning of the story. When you read the story with that in mind, you are considering Hawthorne's diction.