Before we get too far down the form and meter road, gang, we should acknowledge that this is a poem in translation. Neruda wrote the manuscript for Book of Questions in Spanish (he was Chilean, after all) and then it was later translated into English by writer and fellow poet, William O'Daly. That means that the rhythms of the poem in English won't exactly match the Spanish original. (The same goes for the poem's sounds—check out "Sound Check" for more.)
You know what, though? It's not that big a deal. That's because both the English and the Spanish version of this poem are written in a form called free verse. That means, simply, that there are no repeating metrical or rhyming patterns to hang your hat on (or, you know, tune your ear to).
This makes sense when you think about it. Our speaker is putting these questions to us, the readers, directly. In that way, he's involving us in a direct conversation, and free verse is the perfect poetic form to mimic the ebb and flow of natural human speech. After all, when's the last time you had a chin-wag with someone speaking in iambic pentameter?
So, we don't have much going on here metrically, but we do notice that that form of this poem tends to be pretty regular. We get four stanzas of two lines each. (A two-line pair in poetry is called a couplet.) What's more, each stanza asks just one question, but breaks that question halfway through. By dragging the reader along to the next line with the question's continuation, Neruda is making use of enjambment.
This technique does a couple of things to the reader. The first thing it does is add a bit of momentum to the poem. Each odd-numbered line is a kind of cliffhanger, and so we hustle along to the even-numbered line for the resolution of the question. But we don't sprint there (maybe it's more of a power-walk), necessarily. That's because these enjambments actually break the lines in provocative places. Take a look at the third stanza to see what we mean:
Who hears the regrets
of the thieving automobile? (5-6)
Now take a look at line 5. Sure, we know that this question is all about cars gone bad, but what if somebody just asked you, "Who hears the regrets?" That's a pretty profound (and pretty different) question to ponder (maybe it's priests, or judges?). By breaking the line where he does, Neruda allows that question to linger in our mind for just a beat, before we plunge into the specificity of the "thieving automobile" in line 6. He does this in the other stanzas as well. Try covering up the even-numbered lines and reading this poem again. How do those questions change for you?
The poem's form, then, is all about maximizing the impact of the questions it's asking. We're drawn into this conversation, told to give some answers, and then presented with a series of provocatively-posed noodle-scratchers.