(Mostly) Iambic Pentameter Sonnet
Like so many poems in English, this one is written in iambic pentameter. Iambic pentameter is very common, and you can read what Shmoop has to say about it right here. If you don't feel like doing that right now, we'll just tell you that a line of iambic pentameter contains five ("pent-" means five) iambs (a beat composed of an unstressed syllable followed by a stressed syllable). An iamb, when voiced out loud, sounds like daDUM (say "allow" to hear an example). So, iambic pentameter gives us the sound of daDUM, daDUM, daDUM, daDUM, daDUM. Line 12 is a good example:
A rosy garland and a weary head.
You might be thinking to yourself, "Excuse me, but what about lines 4 and 14? They appear to have more than the 10 syllables of an iambic pentameter to me." Thank you for pointing that out, Helpy Helperton. Sometimes, when a word ends with a vowel ("the") and the next word begins with one ("indifferent"), one sound is eliminated. We don't say "thee [space] indifferent," but rather "th'indifferent." So, that solves one problem. The other thing about "indifferent" is we don't pronounce it as 4 syllables ("in-diff-er-ent") but as 3 ("in-diff-rent"). So, when you keep these in mind, you end up with a line that reads like this:
Th'indiffrent judge between the high and low.
See? We get to keep our precious, precious iambic pentameter. In line 14, simply pronounce "livelier" as two syllables ("live-lier") instead of 3 and, poof, problem solved.
Aside from these little hiccups, which are standard in most poetry (once you learn them, you won't see them as hiccups anymore), the poem is extremely regular. Pretty much every line is straight up pentameter, with the exception of the first, which begins with two beats comprised of two stressed syllables each (these are spondees). The point of this is to get our, and Sleep's, attention. The heavy stress adds emphasis, and reminds us that the speaker is kind of yelling (note the exclamation point).
(As a little side note, it is possible to, potentially, read these first words as normal iambs—"Come Sleep! O Sleep." There's no right or wrong way to read them. If they're iambs, however, the speaker's plea seems just a little less stressful, a little less anxious. See, isn't it fun to play around with meter and see what you get?)
Okay, so much for the meter, but what about the structure? Well, it's got 14 lines, and every poem that is only fourteen lines is called a sonnet. Yep, any poem with just fourteen lines is called a sonnet. There are several major types of sonnets (Shakespearean, Petrarchan, Spenserian), but for now you need to know that "Come Sleep! O Sleep" doesn't really fit into either one of these categories.
We know this because Sidney uses a different rhyme scheme (ABABABABCDCDEE) than his British and Italian pals—at least, sort of. Most British sonneteers like to end their sonnets with a couplet (EE), so Sidney follows the example of his countrymen in that regard, but what about the rest? Why not just follow the models?
For one thing, it's really cool and fun to do your own thing. Think of it like this. If your friend started drawing pictures of trees, would you want to draw pictures of trees that looked exactly the same? Heck to the no. So that's one reason. The other reason has to do with the basic structure of a sonnet. In some sonnets, the first eight lines (the octet) are a group, and the last six are a group (the sestet). The rhyme scheme of this poem tells us that we should think of the first eight lines as a group (the rhymes hold them together), and the last six as a group.
So why a group of eight and a group of six? While we don't know exactly "why," we can tell you what happens. Usually, there's a change—a tonal shift, a resolution to a problem posed in the first eight lines, a shift in direction—around line 9. This part of the sonnet is called the turn, or volta. In "Come Sleep! O Sleep," the poem definitely changes a little bit here. While the first eight lines are all about how great Sleep is, and how depressed the speaker is, the final six are about what the speaker is willing to offer Sleep in return for the gift of sleep. Not too dramatic of a change, but hey, it's definitely noticeable. And we have the form (and ol' Philip Sidney) to thank for that. Nice.