Revamping the Bond franchise with Daniel Craig by starting with Fleming's first novel was a smart move, and unlike many Bond films, Casino Royale
actually resembles the book. The movie was actually more complicated and action-packed, though. The plot of the novel is very simple: a Russian agent known as "Le Chiffre" foolishly invested and lost a big chunk of money that SMERSH gave him. Since SMERSH isn't known for being understanding about these things, Le Chiffre is desperate to make a quick fortune before they find out; hence he goes to a high-stakes French casino to play baccarat. MI6 gets wind of his situation, and decides that ruining Le Chiffre would be a great coup, since he's the leader of a communist trade union, so disgracing him would both remove him and be a blow to the commies. So they send James Bond to France to out-gamble Le Chiffre.
Yup, that's the mission. Go to a fancy French casino, put some fat stacks on the table, and try to beat the other guy who's actually a SMERSH agent. Of course he does break Le Chiffre's bank, and that's when Le Chiffre gets really desperate, and things get ugly.
If you've seen the movie, you know basically how everything plays out with Le Chiffre, SMERSH, and Vesper Lynd. And yes, the scene with Bond tied naked to a cane chair with the bottom cut out is from the book. Where the book differs from the movie is that Bond isn't such a smug smart-ass while he's getting his balls tickled by Le Chiffre's carpet-beater. Indeed, this is how all of Fleming's novels differ from the movies: Bond is a much more human character than any of his film versions. He feels fear, sadness, doubt, and he wonders whether he's on the right side. But he's still a cold bastard in the end.
I like Fleming's writing. It's blunt and descriptive and full of elegant details but without a lot of backstory. The plots are straightforward, mostly believable, and they cook right along. If you haven't sampled any of the original Bond stories, you should. One thing to be warned of, though, is that if you think the movie Bond is a bit of a misogynist, Fleming's Bond is even more unapologetic about it. Women are silly, emotional things to be used for pleasure (though his love for Vesper belies this), and he's not too enlightened about the non-white people either. But if you can read the stories for what they were and the time they were written, they're quite fun and Fleming does a lot with relatively thin plots.