Breathless, Digressive, Allusive
If pens had to breathe, Tristram's pen would have suffocated to death before he finished his first chapter. He writes like someone who won't stop yammering long enough to breathe or someone who never lets you get a word in. One thing leads to another by a train of associations so bizarre that you might start walking down the stairs and end up by talking about a chambermaid's buttonhole. Whole chapters are written as responses to other writers or philosophers, like Robert Burton, who wrote a long book about depression called The Anatomy of Melancholy in 1621; or John Locke, a philosopher whose ideas about sensory knowledge and the human mind as a blank slate are responsible for a lot of current political and educational thought. Here's a representative example:
Call down Dolly your chambermaid, and I will give you my cap and bell along with it, if I make not this matter so plain that Dolly herself shall understand it as well as Malbranch.—When Dolly has indited her epistle to Robin, and has thrust her arm in to the bottom of her pocket hanging by her right side;--take that opportunity to recollect that the organs and faculties of perception can, by nothing in this world by so aptly typified and explained as by that one thing which Dolly's hand is in search of.—Your organs are not so dull that I should inform you,--'is an inch, Sir, of red seal-wax (2.10).
What's going on here? you might ask. Who is Tristram talking to? Who's Dolly? (And what has it gots in its pocketses?)
Sterne is ever-so-gently making fun of Locke's ideas, but he's also doing something typically Shandean: addressing his reader directly with a casual "Call down Dolly." And then he describes Dolly in detail, from her boyfriend (Robin) to her dress—despite the fact that Dolly doesn't exist. And the point of all this is to make sure that, despite his bizarre writing style, his point becomes utterly clear.
Basically, Sterne's writing style in Tristram Shandy combines obsessive attention to detail with big-picture thinking about the nature of the world and the meaning of life. His digressions and rapid writing let him link up the two, so the contents of a chambermaid's pocket turn out to be crucial to understanding the meaning of life.