"Carrel," a tricky little vocab word to kick this poem off with, means a study cubicle, like you might find in a library.
"You could" introduces us to a hypothetical situation—something that could be happening, but is not actually happening at the moment. For example, "You could be at the movies, but you're studying for English class instead." The first part of the sentence introduces us to the hypothetical, and the second part tells us what's really up.
Who is the "you" in this first line? It could be us, the readers, or it could be someone specific we haven't discovered yet. It's going to be interesting to see why Wilbur chooses to use the second person (the you). Let's read on, shall we?
Turning some liver-spotted page
This is a continuation of the first line. The "you" could be sitting in a library somewhere, reading, but for whatever reason, is not.
The "liver-spotted" just means that the book is probably old and there are yellow or brown age stains on the page—from liquid or coffee or whatever. You know, reading's always better with a good beverage.
Or rising in an elevator-cage Toward Ladies' Apparel
Another hypothetical situation: the "you" could be in a department store or mall, riding the elevator up to the women's clothes section (a.k.a. shopping).
This is the first hint that we get of who the "you" might be. It seems likely that it would be a woman shopping for Ladies' Apparel.
So far, the two "could be" options don't seem to have any relation to one another—reading in a library, or shopping. So far, we've got some pretty ordinary and random activities. Maybe "you could be playing PS1" or "you could be eating Pinkberry" is coming next.
At the end of the first stanza, we're still not sure who the "you" is, what the "you" is doing, or what the speaker is doing for that matter, but for now we're just rolling with it.
Check out the rhyme in this first stanza. The end words in lines 1 and 4 rhyme ("carrel" and "Apparel"), and the end words in line 2 and 3 rhyme ("page" and "cage"). Keep your ears pealed for this throughout the poem. Our spidey sense says Wilbur might be winding up for an ABBA rhyme scheme. Check out more on that over in "Form and Meter."