Learn to write in rhythm. The venerable doctor seemed to be obsessed with rhyming words; the vast majority of his dozens of books feature text made of rhyming couplets. Seuss even went so far as to create words to rhyme. Get used to the sound of writing rhyming lines.
Be liberal in inventing non-existent words. Words like Sneetch, Woset and Blart are trademark Seuss. The doctor liked to draw his creations according to context, usually a bird-like figure with a somewhat human form.
Tie your writing into visual illustrations. Besides his creatures (both real and made-up), Seuss was a master of architectural illustration, as books like "Oh, the Places You'll Go" and "Did I Ever Tell You How Lucky You Are" clearly show. Read these Seuss books to truly understand how he used the image and the word symbiotically to evoke a unique atmosphere.
Use simple language. Although advanced ideas came through in many of his books, Seuss seemed to be writing primarily for children, and as a result, his books are used to teach millions of kids how to read. Don't get too pedantic with your language; keep the rhyming lines short and sweet.
Let your ideas and philosophies come through with subtlety in your books. Seuss introduced political or philosophical ideas into many of his books like "The Butter Battle Book" and "The Lorax," but he didn't make these books primers on politics or the environment. Seuss didn't let the "ethics" of the story lines overpower the whimsy of his images or the music of his writing, and to see what he was saying, a reader has to look beneath the surface to unstated ideas relative to the plot line and the end results for his various characters. This sophisticated method allows Seuss books to be enjoyed by a wide variety of readers of all ages.