You know you're going to get some crazy language in a book that's all about experimentation. And sure enough, Calvino seems to enjoy showing off his writing agility, moving from short, punchy passages to really long philosophical meanderings on a whim. Overall, he leans a little bit more toward longish sentences, although his educated and playful tone keeps them charming—we promise.
Calvino can be almost journalistic in his simplicity:
So here you are now, ready to attack the first lines of the first page. You prepare to recognize the unmistakable tone of the author. No. You don't recognize it at all. But now that you think about it, who ever said this author had an unmistakable tone? (1.21)
But just as often as you find passages like this, you'll also find ones like this [WARNING: what you are about to read is all a single sentence]:
Little by little you will manage to understand something more about the origins of the translator's machinations: the secret spring that set them in motion was his jealousy of the invisible rival who came constantly between him and Ludmilla, the silent voice that speaks to her through books, this ghost with a thousand faces and faceless, all the more elusive since for Ludmilla authors are never incarnated in individuals of flesh and blood, they exist for her only in published pages, the living and the dead both are there always ready to communicate with her, to amaze her, and Ludmilla is always ready to follow them, in the fickle, carefree relations one can have with incorporeal persons. (13.113)
By varying his sentences so drastically, Calvino is essentially teasing you along his narrative like a fisherman teases a hooked bass. He'll cut you some slack and give you a few paragraphs of easy reading; then he'll jerk the line as hard as he can and bombarding you with long, conceptual sentences that never seem to end.
Let's just hope he doesn't go too far and snap the line, making you chuck his book into a fireplace.
P.S. Don't forget, this book was written in Italian, so in order to really grasp the original style, you're going to have to andare a Roma and brush up on your skills.