I have read both the book and movie of this as well. The movie is somewhat the same as the book, but there are significant differences. Which makes sense as I guess there was a radio version and a book and a computer game and they were all a little different.
But what's the same is that there's a guy named Arthur Dent who's just a normal bloke in a small town in England. His home is about to be bulldozed when his mysterious friend Ford Prefect tells him that the whole Earth is going to be bulldozed. Ford reveals he's an alien working for the publisher of a book called the Hitchhiker's Guide to the Galaxy that's kind of a universal Frommer's travel guide. Ford and Arthur manage to stow away on an alien ship only to be expelled into space, where they're picked up by the galactic president, who has stolen a ship called the Heart of Gold, along with a girl Arthur had a crush on.
The movie is a little more involved in that they have to go get some gun that can make people feel the same as the user. It also plays up the relationship between Arthur and Tricia or Trillian, which I think was an improvement over the book. But they both have a lot of great jokes about the wacky aliens in the galaxy. The movie even manages to work in a few of the asides that made for some of the best jokes in the books.
You can watch either the book or the movie. They're different enough that it's a different experience. Personally I'd recommend both, though the movie takes less time. Douglas Adams wrote the book and worked on the movie, though he didn't live long enough to see it finished.