There’s nothing too crazy going on in this poem—metrically speaking, that is (we’ll leave it to you to determine if all that business about washing the dirty book-child’s face is a little nutty or not). Anyway, the poem is written in that most famous of English meters, iambic pentameter. What’s iambic pentameter? It’s a line that contains five (penta-) iambs. An iamb is a type of beat (sometimes called a foot) that contains an unstressed syllable followed by a stressed syllable. If you say “allow” out loud, you’ll hear an iamb in action: daDUM.
“The Author to Her Book” has some of the neatest iambs ever written. In fact, some of these could be listed in a textbook under the definition of iamb. Take a look at line 21:
And take thy way where yet thou art not known.
If you read this aloud, you should hear iambic pentameter: daDUM daDUM daDUM daDUM daDUM.
While this poem is composed almost entirely in iambs, there is the occasional metrical hiccup, as in line 5:
Made thee in rags, halting to th' press to trudge.
This line contains three different beat types alone: an iamb (“in rags”), a trochee (“Made thee,” “halting”), and an anapest (“to th’ press”). A trochee is simply the reverse of an iamb, and it's usually employed to add emphasis (notice how heavy the line sounds because it begins with “Made”). An anapest, while rare-ish in English, allows the poet to throw in a few extra words here and there and dazzle those with an eye—er, ear—for meters.
These occasional variations, along with the poem’s strict iambic pentameter and rhymes (it is composed entirely of couplets, with no exceptions), show that the poet is in fact very competent. Despite all her complaining about this and that, especially in lines 15-16 (more on those in a moment), this “author” does in fact possess a remarkable command of meter. There is no line in this poem that does not contain five beats (“feet”), or can’t be explained according to very regular rules.
In fact, this is one of those poems, like Coleridge’s “Metrical Feet,” that actually themacizes the whole issue of poetic meter. Check out lines 15-16:
I stretcht thy joints to make thee even feet,
Yet still thou run'st more hobbling than is meet.
The speaker describes the difficulty and violence involved in writing lines of poetry: making words fit the meter is a kind of “stretching,” an attempt to “even” things out that doesn’t always work. Although the speaker claims that her poems still tread on “hobbling” feet, this seems more self-deprecatory than true. There’s no “hobbling” that we can detect! The poem’s meter is actually very “meet,” as you now know if you’ve read this far. In terms of its form, then, this poem is a success, which underscores the possibility that all the speaker’s complaining is for show, and not really genuine.