The poem is divided into five 4-line stanzas, called quatrains. Each quatrain has an ABAB rhyme pattern (look at the first quatrain: "stay" rhymes with "say," and "wings" rhymes with "things").
The meter is a little bit tougher: there isn't a rigidly set number of syllables per line, like you'd find in a sonnet. Notice how long all the lines are – in some editions of the poem, there isn't even enough space to fit all the words in each line, so they spill over into the next (if you thought your edition was numbering the lines wrong, that's what's going on). It's as though the speaker wants to stretch out each line as long as possible – and for a poem about the passage of time and the inevitability of death, we can't really blame him for wanting to drag his feet a little.
The lines that are in quotation marks – the last line or two of each stanza – are hardly in verse at all. Because the poet is imagining what his neighbors would say, those lines almost read like prose, or regular, conversational dialogue.