Whitman's particular style of writing has come to be known as "free verse," but not everyone agrees with this term. The term "free verse" was popularized by 20th century poets like William Carlos Williams and Allen Ginsberg whom Whitman inspired. The term means "a poem with no regular form or meter." If that's the definition, then "Song of Myself" is free verse.
Other critics prefer not to use the term "free verse," arguing that Whitman borrows forms and styles from all over the place. According to this train of thought, labeling Whitman's poetry "free verse," would cover up this vast diversity styles he draws from.
Either way, we don't think it's a huge deal. Technical terms in poetry can be overrated.
Besides, a verse of Whitman's poetry is recognizable from a mile away. He uses tons of repetition, including the repetition of words at the beginning of lines, called "anaphora." His stanzas are frequently long lists, called "catalogues." And his lines are generally longer than those in most other classic poems.
As we mentioned, Whitman does not use a regular meter, but his ear for rhythm is probably his greatest poetic strength. At some points he seems to slip into a traditional use of stresses and beats, as in this phrase from Section 1:
Hous-es and rooms are full of per-fumes
More often, though, he uses sharp beats at random, like someone reciting a hypnotic chant from Section 8:
The blab of the pave . . . . the tires and carts and sluff of boot-soles and talk of the prom-en-ad-ers
Gallons of ink have been spilled on Whitman's peculiar sense for rhythm, and your best bet is to explore the poem on your own.
Finally, the original edition of the poem was not divided into sections. Whitman simply used stanzas of varying length and changed from topic to topic without warning. In the 1867 edition of "Song of Myself," he divided the poem into 52 sections, and we use these sections to make it easier to refer to specific parts of this very long poem. These sections often center on a specific topic or vignette (mini-story), but they are somewhat arbitrary. If you have a version with section divisions, we recommend you also try reading one without the divisions. Viewing the poem as an organic and ever-changing whole can be a refreshing and liberating experience.