This page is Superman's biography from the comic books continuity which ended in 1985 with Crisis on Infinite Earths.
Baby Kal-El was born to Jor-El and Lara on the planet Krypton. Shortly after his birth, his father placed him in a space-ship model he had constructed, as he had run out of time to build a full-size ship to carry the whole family off the planet. The ship was launched, and traveled through interstellar space towards Earth. ("The Origin of Superman")
His rocket landed in rural Smallville. There, he was found by Martha and Jonathan Kent, who soon took him to the orphanage. In the orphanage, the baby performed amazing feats of strength, frightening the staff. When the Kents returned the next day to adopt him, the staff were only too happy to be rid of the uncontrollable baby. The kents named him Clark, after Martha's family, the Clarks. ("The Origin of Superman")
The Kents soon discovered the amazing powers their adoptive son had. He was seemingly invulnerable, faster than a locomotive, and able to leap amazing distances. ("The Origin of Superman")
As Clark approached adulthood, Martha grew ill and died, and Jonathan soon after. On his death bed, Jonathan made Clark swear to use his powers for good. Clark soon adopted the identity of Superman, to make good on his promise to his father. ("The Origin of Superman")
When Clark Kent and Lois Lane accompanied a new space rocket to cover its maiden voyage, Brainiac appeared and attacked. Superman slipped out of the rocket, and engaged Brainiac, but was confounded by his high-tech weapons and forcefields. Brainiac shrunk Metropolis and added it to his collection of shrunken cities. Superman rescued Metropolis, as well as Kandor, a surviving Kryptonian city. Superman added it to his fortress, pledging to one day enlarge it. ("The Super-Duel in Space")
Jimmy Olsen, having been granted three magical wishes, used them in an attempt to repay Superman for his heroics. One of his wishes lead to the creation of a Supergirl, who failed to be very helpful to Superman and ended up sacrificing herself to save his life. ("The Girl of Steel")
Superman met his cousin, Kara Zor-El, who had crash-landed outside Metropolis. She told him the story of how she survived Krypton's destruction. She became the new Supergirl, and Superman put her into the Midvale Orphanage, where she would live under the name Linda Lee. ("The Supergirl from Krypton")