Oedipus was the child of Laius and Jocasta, the tuling couple of Thebes. The oracle at Delphi gave them the news that their newborn son would grow up to kill his father and marry his mother.
Lauis gave his son to a herdsmen and ordered him to be killed.
A spike was driven through Oedipus' ankles (causing his ankles to become inflamed and earn his name, which translates to "swollen-footed"). The herdsmen took pity on the baby and gave him to a herdsmen from a far off kingdom instead of letting him die.
Polybus and Merope raised Oedipus as their own, but one night Oedipus could not shake the fact that he had no idea who his parents were, so he went to the Oracle to find out.
The Oracle, however, did not tell him who his parents were, but only the original prophecy that would come true. In an attempt to save his "parents," Polybus and Merope. He set off to a new kingdom.
On his journey, another driver struck Oedipus so he would move out of the way. The two ended up in a serious fight, in which Oedipus killed the other driver, who was actually King Laius. He had fulfilled half the prophecy without realizing.