"Ariel" is written in free verse, which means that it has no regular rhyme scheme or meter. That doesn't mean that "Ariel" is a willy-nilly mess, though.
Plath's poem is organized into tercets, or three-line stanzas. And Plath's lines, though not metered, are almost all short and clipped. The poem itself is 31 lines long, but when you read it aloud, you realize that it goes by pretty darn quickly. (Check out "Sound Check" for more on the other stuff you hear when you read this poem out loud.)
While there is no regular rhyme scheme in "Ariel," there are rhymes all over the poem. Some are full rhymes—like "air" (16) and "hair (17) and "I" (19) and "cry" (21)—and others are slant rhymes, such as "flies" (25) and "drive" (26). The rhymes may not come regularly in this poem, but they come frequently. "Ariel" is known for the density of its language—the way both the sounds and the images pile up in such a confined space—which really adds to the speaker's jumbled sensation as she's bounced around on the top of a runaway horse.
"Ariel" is also known for its enjambments, or line breaks that end before the finished thought, pulling the reader along into the next line. Examples, you demand? Well, there's a pretty extreme enjambment at the end of the poem:
Into the red
Eye, the cauldron of morning. (30-31)
See how Plath separates the descriptor ("red") from the noun it's describing ("eye")? It's a bold and daring line break (or, to be more exact, a bold and daring stanza break). Enjambments like these add to the hurried, jerky, uncontrollable, and uncontrolled feeling that we get when we read the poem. Plath knew how to make her form echo her content.