Following a disastrous libel case that cost him his credibility, a large chunk of money and eventual jail time, disgraced journalist Mikael Blomkvist (Michael Nyqvist) takes on a freelance detective job for Henrik Vanger (Sven-Bertil Taube), an aging, wealthy former titan of industry who searches for his niece who disappeared 40 years earlier.
Mikael discovers Vanger hired him based on a surveillance report written by Lisbeth Salander (Noomi Rapace), the titular character of the book and film. Salander is eventually tracked down by Blomkvist, who takes her on as both his love interest and partner in tracking down the missing girl (her incredible computer hacking skills come in handy more than once).
Salander has a shady past that haunts her day to day life and is further examined in the subsequent sequels The Girl Who Played with Fire and The Girl Who Kicked the Hornet's Nest. Because of her past, Salander is in the care of a guardian, been in and out of mental hospitals for years and while the film hints at her ‘crimes,' it would have served the filmmakers better had they told the events in the follow up films as they were written in the novels.
Rapace definitely looks the part of Salander, but is too open and expressive as opposed to her character in the book. Nyqvist is physically not how I pictured Blomkvist thus creating problems for me to accept him in this part. Some characters, like Blomkvist's work partner, Erika Berger and Salander's original guardian, Holger Palmgren, are either given extremely small parts or written out of the movie entirely, which is odd because later in the series they become very important to the overall plot.
My suggestion is to read the book; it is, of course, better than the film. But if you'd rather see the movie instead, Oplev, even with some glaring errors and plot-holes, does a somewhat admirable job in adapting Larsson's complex novel to screen. The audience comes away with a general idea of the author's message.