Let's start with the obvious question: I have read the book, but not since high school, so this will not be the place for a point-by-point comparison or a list of all the ways in which Luhrmann has changed things. And even if the book were fresh in my mind, those things wouldn't interest me much, because this is a movie, and it should be judged on its own merits, on whether it succeeds or fails as a movie.
That said, The Great Gatsby is a novel whose reputation is based largely on Fitzgerald's prose, and so it's notable that Luhrmann's most obvious major change allows him to get more of that prose into the movie. Luhrmann has added a framing story which finds Nick Carraway (Tobey Maguire) in a sanitarium, recovering from some sort of breakdown (the doctor's notes list his symptoms as insomnia and "morbid alcoholism"); his doctor encourages him to write about his memories as a way of exorcising them, and we hear large chunks of Nick's story (which is, of course, Fitzgerald's novel) as voice-over narration.
That story centers on Nick's cousin, Daisy (Carey Mulligan), and his neighbor, Jay Gatsby (Leonardo DiCaprio). Gatsby is a mysterious member of the nouveau riche; no one is quite sure where he (or his money) came from. Daisy lives across the bay with her old-money husband, Tom (Australian actor Joel Edgerton, doing an American accent that is an unfortunate blend of Ernest Hemingway and Foghorn Leghorn). Gatsby throws spectacular weekend parties, at which anyone who's anyone simply must be seen.
Those parties are a fine example of both what's good and what's bad about the movie. They are, as you'd expect from Luhrmann, visually spectacular, and the use of anachronistic music helps to make that excitement feel new and of the moment, and to make Gatsby's world seem like a place that is entirely alien to Nick. (The fact that most of the music comes from the modern R&B/hip-hop world only emphasizes Nick's disconnection, because Tobey Maguire is among the leading contenders for the crown of Whitest Man in Show Biz.) But for all the energy and visual excitement, the parties aren't enticing. You sense that people have shown up because doing so is socially obligatory, not because they're having any fun.
The other visuals of the movie are also marvelous (costumes and production design are both by Catherine Martin). One thing that period movies often get wrong is that everything looks old, a bit drab and faded, as if the period has been re-created with objects that actually are that old; even if the movie's in color, everything is tinged with sepia. Martin and Luhrmann don't make that mistake; they remember that these characters are wealthy, and that everything they own will be new and bright and shiny.
(I should mention that the movie is in 3-D. I can't do 3-D because of vision issues, so I can't offer any useful commentary on that aspect. It did seem to me, though, more so than most 3-D movies, that the technology often makes the actors look slightly creepy and puppet-like.)
The strongest scenes in the movie are not the noisy party scenes, though; they're the quieter character moments, particularly from DiCaprio. He does lovely work in a scene where he's nervously anticipating his reunion with Daisy, and the explosion of anger that marks his final confrontation with Tom is chilling. He's also (finally!) beginning to age into a mature masculinity; he's a handsome man in this movie instead of the pretty boy he was for so long.
And because the movie's stronger when it's actually telling the story, rather than when it tries to dazzle us, I think you're likely to enjoy the movie more as it goes along. The opening, when we're being teased with the parties and the glitz and the mystery of Gatsby, is far less interesting than the last 45 minutes or so, when the truth about these characters and their relationships is finally revealed.