There's quite a bit, but let me sum up...
In the movie, the story is being read by a grandfather to his sick grandson, and that's all there is to it.
In the novel, the setup is close but not quite. The author states (lies) that the novel is an abridgement of a much larger satirical renaissance work subtitled "S. Morgenstern's Classic Tale of True Love and High Adventure". It was (still lies) the book that his father read to him when he was a child, but skipped bits he considered to highbrow or boring for a kid. His abridgement is in theory is an attempt to recreate that experience out of the original work, with running commentary on what gets skipped and musings on his experiences. This means the novel reads a lot like the movie - as in, with many interruptions - but the interruptions are usually more adult-minded than "Is this a kissing book?".
In the movie, the Pit of Despair is just a hidden room underneath a grove of trees. It's a well-hidden torture chamber, but that's it.
In the book, the Pit of Despair is the bottom room of a multi-level dungeon named the Zoo of Death, containing all of the many many lethal creatures Humperdinck has demonstrated his strength against. Inigo and Fezzik have quite a bit of work to do to get to Westley. There is a good bit where a deadly trap of doooom awaits our heroes at the bottom (a deadly spider hiding in the doorknob), but Fezzik either being genre-savvy or fourth-wall-aware gets scared and just beats the door down.
- The setup and the Prince gets more screen time
In the movie, the opening moves swiftly along and despite the intervening years Buttercup is engaged to Humperdinck mere minutes after Westley is murdered by pirates.
In the book, Humperdinck has small bits of plot to set up the later hijinks, where he rejects Guilder's princess, approaches Buttercup to propose (which she treats with disdain, but having few choices accepts), and everything's more fleshed out by the time we get to high adventure. Humperdinck himself is portrayed as a mighty hunter and a "man's man" without peer, but this is tied into his ultimate flaw, cowardice, and shown to be vain attempts to demonstrate his dominance against things he knows he can beat. Most of the bits that Goldman fake-skips are early on as well, so there's more interruptions as he explains that forty pages of Florin history and sixty on the attempts to restore the old King's health are useless bunk, as is Buttercup's time being princess trained and Humperdinck wrangling the nobles into accepting the marriage.
Much of the rest of the cast gets their buildup too (as @FuzzyBoots notes in comments). Rugen's reasons for seeking Inigo's father out are clearer; his having six fingers isn't just an identifier, it's a handicap to the balance of a master swordsman, thus the point of his special commission. Fezzik's childhood as an utterly gentle soul is gone into, and that turns out how you'd expect.
- And then there's the ending...
The finale matches the movie quite a bit, but I'd be remiss if I didn't mention that the author finds out that his father skips the final section of the tale, where while riding off into the sunset, Westley relapses and falls off his horse, Inigo's wounds reopen, Fezzik tries to lead and takes a wrong turn, Buttercups horse throws a shoe, Humperdinck and his hunting party can be heard catching up, and so the adventure continues on a very bleak ending note.
There are even notes in some editions of the (still fake) sequel titled "Buttercup's Baby" that the author is fighting with Morgenstern's estate to get the rights to.
To finish up, a bunch of little things...
- The book uses shark-infested waters, not shrieking eels, although the sharks do make a surprising ruckus.
- It is made clear that Westley was watching Buttercup just before her kidnapping.
- Vizzini does have some actual clever moments, but is clearly in delusional denial as soon as his plans start to fall apart.
- Fezzik has plenty more lines, and is often pointing out exactly how stupid Vizzini is being by trying not to argue with him.
- Most of the chase sequence actually happens at night.
- Vizzini actually talks a lot more (surprise) about how smart he is as he loses the Battle of Wits. He's smart enough to keep his knife at Buttercup's throat though, and Westley does more acting to play upon his overconfidence.
- Westley gets quite a few more moments of genuine anger sprinkled here and there, and during the finale actually roars at Buttercup to do what she's told (tie up Humperdinck, preferably before he collapses).
- There's plenty of Westley torture before Rugen gets to the Machine. Humperdinck helps too. The max setting was 20, not 50 though.
- There's a quest for Fezzik and Inigo to find ingredients for Max (also courtesy of @FuzzyBoots), but this is also one of the author's fake-skips.
Finally finally, I should also note that lots of the dialogue is lifted straight from the novel, although some of it is in slightly different order. Almost every classic and quotable film line is in there (except Miracle Max, but even that's closer than you'd expect to Billy Crystal's improv), and I had started a list of similarities before it grew too large and silly to address.