What you need to know about the story in Sophocles' Oedipus, The King:
Prophecies say the yet unborn son of Laius, king of Thebes, will grow up and kill him. When the baby is just three days old Laius binds the baby's feet and gives it to one of his shepherds to leave on a mountainside to die. Unbeknownst to Laius, the shepherd takes the baby and gives it to a friend of his from a neighboring kingdom. This man then gives it to the king and queen of that land, since they are childless. They raise the baby as their own son, naming him Oedipus and telling him nothing of his origins. When Oedipus has grown, he hears a drunken man accuse him of not being the true son of those he believes to be his parents. He consults the oracle and is told he is destined to kill his father and wed his mother. Oedipus leaves the kingdom he grew up in so as to avoid this terrible fate. At a place where three roads meet he encounters a small party of travelers who attempt to push him off the road; he responds by killing all but one of the party. He continues on to the city of Thebes, which is without a king and suffers at the hands of a sphinx who demands that the young men of the city answer her riddle correctly or die. When Oedipus figures out the riddle, the people of Thebes make him their king, and Oedipus marries Jocasta, the widow of the King who had died shortly before Oedipus arrived in the city. Years pass, Oedipus has sons and daughters by Jocasta, and is a king well liked by the people of Thebes; but a plague has come upon the city and the people ask Oedipus to discover what can be done. The oracle at Delphi says that the murderer of the previous king, Laius, is living among the people of Thebes and must be cast out in order to end the plague. Oedipus vows to discover the murderer and exile him. Creon, Jocasta's brother and joint ruler of Thebes, suggests that Oedipus consult with the blind seer, Tiresias. But when Tiresias tells Oedipus that he, himself, is the man he seeks, Oedipus accuses Creon of conspiring against him. Creon defends himself, claiming he is happy sharing equal rule with Oedipus and Jocasta. Jocasta tells Oedipus all she knows about her former husband's death, specifically that it happened where three roads meet. Oedipus begins to suspect he might actually be the murderer of Laius and sends for the shepherd who survived the incident at the crossroads, to question him. At the same time, a messenger from the neighboring kingdom arrives and tells Oedipus that the king who raised him as a son has died and the people what him to be king there too. Oedipus dares not go back because of the prophecy that he will wed his mother, but the messenger reassures him that he need have no fear, since he knows she is not Oedipus's real mother. It turns out the messenger is the very man to whom Laius's kindhearted, but disloyal, shepherd gave the baby that he was supposed to kill. The shepherd that survived the roadside attack arrives and reveals all. Jocasta realizes that Oedipus is indeed her son and retreats into the palace. When Oedipus is finally convinced that not only did he murder his true father, Laius, but has also wed his true mother, he follows Jocasta into the palace. A servant from the palace recounts to the people of Thebes how Oedipus came in to the palace raging, battered down Jocasta's door, and found her lifeless body; for she had hanged herself. When Oedipus saw this he reached for the two broaches from Jocasta's dress and used them to gouge out his eyes. Oedipus promises to leave Thebes forever to rid it of the corruption that has caused the plague. He says goodbye to his two young daughters and leaves. The chorus of Thebans laments that we should count no man happy until he dies free of troubles.
