Warning: Wikipedia contains spoilers.
The first movie begins with the titular character - John Rambo, played by Sylvester Stallone - returning from the Vietnam War and searching for an old Army buddy. After discovering that his friend had died of cancer, and being escorted to the town limits by the local sheriff (Brian Dennehy), Rambo walks back to the town. The sheriff then arrests him and during a "forced" shower with firehose, Rambo is reminded of his experience as a POW in Vietnam. This causes him to temporarily lose touch with reality. Rambo escapes from prison and hides in the local mountains.
The sheriff tries to "hunt" Rambo down; however, Rambo is better trained for this, and continuously eludes the posse (killing some of his pursuers in the process). The Army sends Colonel Trautman (Richard Crenna) to help the sheriff capture Rambo. The sheriff refuses help, worried that the Army is trying to protect their "asset." Trautman informs the sheriff that he isn't trying to protect Rambo from the sheriff, but to protect the police from Rambo.
After much mayhem and murder, Rambo is finally arrested. (In the novel, Rambo dies.)
The second movie has Rambo leaving prison to rescue some POWs in Vietnam, while the third sees Rambo going to Afghanistan to rescue Colonel Trautman.
There is also a David Morell novel of the second movie, but unlike the first book this was written after rather than before the movie.