Goku is one of the few remaining Saiyans in the world. His real name is Kakarot which is what the remaining Saiyans call him.
He was sent to Earth when he was a baby to prepare the auctioning of it, but Goku fell into a ravine, lost his memory and forgot his mission.
Goku is then raised by an elderly old man named Gohan who teaches him the basics of karate. Gohan is later killed by Goku accidentally.
All Goku can remember is his grandfather telling him never to look at the moon again.
Goku eventaully meets Bulma, a girl searching for the mystical dragonballs. Goku has a dragonball, but refuses to give it to her.
He does eventually join Bulma in the search. Goku is not good at anything other than fighting. He is the best fighter to ever live.
Goku is trained by Master Roshi for a time, and then King Kai after the Saiyan Saga.
This training gives Goku the most techniques of any of the Z warriors. Goku marries Chi-Chi at the end of Dragonball (the daughter of Ox-King),
and they have two sons: Gohan and Goten.