Prose in a Dr. Seuss book? What is this, opposite day? Don't worry; it's not opposite day. Unless, of course, it is opposite day, in which case we'd have to tell you that it wasn't opposite day. Then again, if it wasn't opposite day, and we told you it wasn't…
Well, be it opposite day or no, The 500 Hats of Bartholomew Cubbins is written in prose. As such, we have nothing to say about stanzas, enjambment, anapestic tetrameter, and other poetic devices this time around. To those few who truly enjoy that stuff, we are sorry.
As for reading it aloud, here we'd recommend reading it like all other Seuss works—in effect, just have fun with it. No need to make this a solemn occasion, reading it with that slow, toneless reverence one might read The Waste Land with. Instead, do voices, inflect all over the place, and really exclaim those exclamation marks. Exclamation points? Whatever.
And when in doubt, improvise. It's not like you have worry about what an anapest is this time around, so just go for it.