The style of “Young Goodman Brown” is fairly typical of 19th-century Romantic literature (particularly Dark Romanticism) in several ways. For one, Romantic literature is known for lush descriptions of nature, and Dark Romanticism is known for locating evil in nature. Hawthorne does this throughout "Young Goodman Brown," but here is one example:
At one extremity of an open space, hemmed in by the dark wall of the forest, arose a rock, bearing some rude, natural resemblance either to an altar or a pulpit, and surrounded by four blazing pines, their tops aflame, their stems untouched, like candles at an evening meeting. The mass of foliage, that had overgrown the summit of the rock, was all on fire, blazing high into the night, and fitfully illuminating the whole field. Each pendent twig and leafy festoon was in a blaze.
Another characteristic of Romantic literature is its interest in the human psyche, and particularly in creating physical places or journeys that mirror a character's mind. In "Young Goodman Brown," Goodman Brown takes a journey into the forest, but it's also a journey into his own mind and heart. When he finds evil lurking in the forest, he's really discovering that he himself is a sinner, as he chose to go into the wilderness and meet the devil.
Another key facet of the story’s style is its use of dialect. While written in the 1830s, the story is set in the late 1600s, and for this reason, the characters’ dialogue is markedly old fashioned. For instance, characters use “thee” and “thou” when they speak, which is not how ordinary people would have spoken in Hawthorne's day. This stylistic choice has two effects: first, it places readers more firmly inside the story's setting, and second, it evokes biblical language, which plays on the story's central themes of sin and loss of faith.