The form of this poem doesn't have a specific name, but it is very formal. The poem is constructed of three ten-line stanzas and each stanza is constructed the same way.
Lines 1, 5, and 6 of each stanza are iambic tetrameter, meaning they have eight syllables with four of them stressed. Line 2 is in dimeter, meaning it has four syllables, with two stressed. The rest of the lines are the more standard iambic pentameter—ten syllables, five stresses.
Here's a quick breakdown of the first stanza with the stressed syllables highlighted. You'll notice that the meter isn't perfect—perfection is boring. Variety is the spice of life.
Busy old fool, unruly sun,
Why dost thou thus,
Through windows, and through curtains, call on us?
Must to thy motions lovers' SEAsons run?
saucy pedantic wretch, go chide
Late school-boys, and sour prentices,
Go tell court-huntsmen that the king will ride,
Call country ants to harvest offices;
love, all alike, no season knows, nor clime,
Nor hours, days, months, which are the rags of time.
The variation of line length and the meter allows Donne to achieve some special effects. Most noticeably, the short lines allow Donne to hammer home two sarcastic, rhetorical questions and then level his striking proclamation: "nothing else is." That line also varies from the iambic rhythm by giving us a spondee (two stressed syllables back-to-back) in the last foot.
Other variations include some trochees at the beginnings of the lines. That's where you emphasize the first syllable of the metrical foot. In doing this, Donne's speaking voice becomes more pronounced and powerful. Donne starts the poem with one of these: "busy old fool." It gets the poem off and running. The next-to-last line also starts this way, emphasizing the first word: "shine here to us, and thou art everywhere."
The rhyme scheme of each stanza (ABBACDCDEE) is a quirky mix of two types of sonnet forms, the Petrarchan and the Shakespearean. The first four lines follow the Petrarchan sonnet and generally set up the new argument or image, including rhetorical questions. The next four conform to the sort of sonnets becoming popular during Donne's lifetime, and they extend the image and provide some sort of proof or answer for the argument. The final couplet, being an easier, more obvious rhyme, seals what was previously stated in a strong and memorable way. The final lines of the poem demonstrate this sense of closure. Argument? Won.
For more on how this form and meter is working all kinds of magic for Donne and his poetic mojo, check out our "Sound Check" section.