Warning: Wikipedia contains spoilers.
As in the comic series, Superman is the last survivor of the planet Krypton who as an infant was sent to Earth by his parents Jor-El (played by Marlon Brando for a payment, notorious at the time, of $4 million for eight minutes' screen time) and Lara. He's raised by Jonathan and Martha Kent in Smallville and upon reaching adulthood takes a job as a reporter for the Daily Planet newspaper in Metropolis. It is in Metropolis that he first appears publicly as Superman. He gives an interview to Lois Lane and comes to the attention of Lex Luthor, a criminal mastermind who has secret headquarters in Metropolis' subway system.
Luthor has reprogrammed two ICBMs with nuclear warheads to hit the San Andreas Fault and Hackensack, New Jersey; his objective is to cause a major earthquake in California that will cause most of the state to slide into the ocean. Superman is at first weakened by Kryptonite that Luthor discovered in Addis Ababa, but he escapes with the help of Luthor's girlfriend, who makes him promise to first stop the missile headed for Hackensack. He fulfills his promise, steering the Hackensack missile off course into the sky, but then sees the nuclear explosion from the California missile. This explosion causes an earthquake in which Lois Lane, who's out there for the Daily Planet, is killed.
Fraught with grief, Superman flies at super-speed, travelling back in time and rescuing Lois from the earthquake. Superman flies Luthor and his henchman (played by Beatty) to jail, and the movie ends as the hero flies "up, up and away".
The film was awarded a Special Achievement Academy Award for its visual effects, and led to four theatrical sequels - Superman II, Superman III, Supergirl, and Superman IV: The Quest for Peace. The film's legacy includes numerous television series, notably Superboy (produced, like the movie, by Alexander Salkind), Lois and Clark: The New Adventures of Superman, Superman: The Animated Series, and the current prequel series, Smallville, which have all been influenced by the movie to some extent.