The movie was very faithful to the book, as others here have stated. I have listed a few major points below, along with my recommendation regarding your particular problem.
The movie does make a few missteps, however. The relationship between Katniss and Peeta is frankly misportrayed as a mutual romance, perhaps in an attempt to capitalize on the "love triangle" trope popular in adolescent fiction currently. Gale's role in Katniss' life is downplayed almost completely, in order to promote Peeta's role. Some details regarding the games are fudged for clarity; it's hard to show how Haymitch wordlessly communicated with Katniss through gifts from a third person view, so they show him sending actual written messages. Certain plot points from Catching Fire concurrent to The Hunger Games carry over into the movie, while in the books they are a surprise kept for the second book. Overall, though, the movie is an excellent depiction of the events of the book, if not the characters.
My wholehearted recommendation as a fan is to read the whole book first, however. The book is written from Katniss' perspective, while the movie is obviously written from a third person view, the cameras seeing the events. Since you don't have Katniss' perspective on the events of the movie, you may not draw all the same conclusions from certain events as she does, particularly during the games themselves. This can lead to some misunderstandings, particularly in view of Katniss' motivations and feelings. Her character is very strongly written, and it is hard to grasp her fully just by watching.