Let's start with the easy stuff. The poem is comprised of four quatrains. That means the poem is made of four different stanzas that each have four lines apiece. Rhyme scheme is next. The rhyme scheme of each stanza is ABAB. This means that lines 1 and 3 rhyme with each other, and lines 2 and 4 rhyme with each other. As for the rhythm and meter, that's not quite so straight forward. Most of the poem is written in the iambic foot. An iambic foot contains an unstressed syllable followed by a stressed syllable. I'll use bold to indicate the stressed syllables.
And this | same flower | that smiles | to-day
The first line of the poem is an example of how all of the lines are not made up of all iambs. The first foot is a trochee, and that means the stressed syllable comes first.
Gath-er | ye rose|-buds while | ye may.
Notice how both of the examples have four rhythmic feet. This is called tetrameter. The odd numbered lines are all iambic tetrameter. The even numbered lines are one syllable short. This is called catalexis and results in the even numbered lines of this poem being catalectic lines of poetry. I'll use line 2 as an example.
Old time| is still | a-fly|-ing