(From the Fallout: New Vegas Wikipedia page)
The protagonist is a courier working for the Mojave Express postal service. The game begins as The Courier awakes in the town of Goodsprings after being shot and left for dead by mobster and casino owner Benny (voiced by Matthew Perry) and his goons. They have robbed The Courier of the "Platinum Chip" which The Courier was to have delivered to New Vegas. The Courier is dug out of a shallow grave by Securitron Victor (voiced by William Sadler) and nursed back to health by physician Doc Mitchell (voiced by Michael Hogan). The Courier's main quest is to locate Benny and retrieve the Platinum Chip. Along the way The Courier encounters additional quests involving individuals and groups whom The Courier can choose to assist, ignore, or sabotage, gaining or losing karma and affecting the course of the game.
Eventually, The Courier confronts Benny at his casino on the New Vegas Strip and can choose to dispose of Benny and recover the Platinum Chip or allow Benny to escape. The Courier becomes entangled in the conflict between Caesar's Legion, the NCR, and Mr House for control of Hoover Dam and thus control of the region.
It transpires that Mr House is a human from before the Great War who survived in a life-support chamber. He made the Platinum Chip, containing a Securitron upgrade program, to protect Las Vegas during the war. However, the War began before the Chip was delivered. Benny ambushed The Courier in a scheme to usurp Mr House with the help of a reprogrammed Securitron called Yes Man (voiced by Dave Foley). The Courier has the option to co-opt Benny's plan and claim New Vegas.
Caesar's Legion attacks Hoover Dam led by Legate Lanius (voiced by Mitch Lewis) with the NCR defending under General Lee Oliver. The Courier will either conquer the Dam for Caesar's Legion, defend it for the NCR, or connect the Dam to Mr House's network and evict both the Legion and the NCR.
A narrated slideshow shows the results of The Courier's actions, who comes to power over New Vegas and the Mojave Wasteland, and the fates of the other factions and characters.