This poem has a simple ABAB rhyme scheme, meaning that every other line within a stanza rhymes. Many of the rhymes, though, are slant rhymes (words that almost rhyme, but not quite). Let take a look at the first stanza:
The whiskey on your breath (A)
Could make a small boy dizzy; (B)
But I hung on like death: (A)
Such waltzing was not easy. (B)
The lines with corresponding letters rhyme. The B rhyme in this stanza is an example of a slant rhyme – "dizzy" sounds a bit like "easy," but isn't a perfect rhyme.
Inside of the quatrains (a stanza consisting of four lines), this poem has an intricate rhythm. You may have heard of iambic pentameter, which is a classic five-beat pattern of rhythm. "Iambic" means that a stressed syllable follows an unstressed syllable. And iamb is one unstressed syllable followed by a stressed one. "I am" is actually an example of an iamb. Some people say that an iambic rhythm mirrors the da-DUM sound of a heart beat.
This poem is iambic, but instead of having five stressed syllables per line, there's only three, which makes it trimeter, not pentameter. Think of tri as meaning three – like a tricycle has three wheels. In poetry, trimeter has three beats. Let's look at a line for an example. Stressed syllables are in bold and italic:
The whisk|ey on | your breath
The cool thing about this poem being written in iambic trimeter is that it becomes not just a poem about a waltz, but a waltz itself, because there are three beats in a waltz.