The poem jumps right in without any scene-setting, unfolding in a single sentence enjambed across eight lines. This structure gives the poem tension and an element of surprise, which subtly mirrors the speaker's pleasant surprise at the "dust of snow."
The poem begins with the image of a crow. Crows can be symbolically associated with death, so the first line seems as if it might signal some grim content to follow. But the focus is on "the way" the crow does something, not the crow itself. That is, it's the manner and timing with which the crow performs the poem's main action that so affects the speaker. (As it turns out, this poem is all about timing. The speaker was in a bad mood, and this crow, by sheer chance, was in the right place at the right time to help.)
The first two lines also juxtapose the "crow" with the human speaker ("me"), setting up a subtle contrast between the instinct-driven natural world and the complex interior of the speaker's mind. As the reader learns at the end, the speaker has been lost in thought, "rue[ing]" the day for an unspecified reason. Meanwhile, the crow is just going about its business, unconcerned by the turmoil of human emotion.
Consonance links the hard /c/ sounds at the beginning of "crow" and the end of "Shook," with the harsh repetition perhaps evoking the jostling of the tree. The four /o/ sounds in "crow / Shook down on" are all slightly different, so they're not quite assonant, but the shared vowel links the words visually, making the image more cohesive.
Grammatically, though, the poem is up in the air. A main verb still awaits, as does the object of the verb "Shook down," so for a moment, the reader can only process the few elements that are there. This suspenseful syntax (with the suspense drawn out by line breaks) helps grab the reader's interest and maintain it throughout the poem.