To examine a poem's style, let's first consider two poems with quite different styles. First, these are the opening lines of Edgar Allan Poe's "The Raven":
Once upon a midnight dreary, while I pondered, weak and weary,
Over many a quaint and curious volume of forgotten lore—
While I nodded, nearly napping, suddenly there came a tapping,
As of some one gently rapping, rapping at my chamber door.
“’Tis some visitor,” I muttered, “tapping at my chamber door—
Only this and nothing more.”
For comparison, consider the opening lines of E.E. Cummings's poem "I Have Found What You Are Like":
i have found what you are like
(Who feathers frightened fields
with the superior dust-of-sleep. wields
easily the pale club of the wind
and swirled justly souls of flower strike
the air in utterable coolness
deeds of green thrilling light
It's easy to recognize the differences in style just by the placement of the words on the page, in this case—visually. While Poe relies on a traditional format, with lines placed typically on the page, Cummings scatters his words in an atypical way. Lines may begin on the left, and they may be indented far beyond what is typical. Cummings does not use predictable rhythm or rhyme patterns, while Poe maintains a strict trochaic octameter, with the final line of each stanza becoming a refrain which continues through the poem. Poe's style is careful and tightly constructed, while Cummings's style is open and free to defy and redefine expectations. Cummings is also known for inventing new usages of grammar, so you will notice rather odd placements of periods, non-standard capitalization, and invented words.
All of these choices relate to a poet's style. A poet may vary their style from poem to poem, but generally speaking, style is fairly consistent within a poet's overall body of work. Style is determined in part by rhythm and cadence—or the lack of it. It is also determined by the poem's rhyme pattern and whether the author, like Poe, relies on internal rhyme to deliver the poem's message. A poem's length factors into the poem's style, as does its use of punctuation and grammar. The poem's use of figurative language helps determine its style too. The poet conveys a message by utilizing these various aspects of style to best capture their intended meaning.