Oedipus sends Creon to find out how to rid of the curse, which the oracle says, "Thebes will be saved only by purging herself of the old kings's murderer".
Creon, go find out how to rid of this curse
You must kill the man that killed the king to eliminate the curse
Creon gets the prophet Tiresias who didn't want to talk. When Oedipus accuses him though, then Tiresias believes that Oedipus is the killer. and in an act of rage, Oedipus accuses Creon of the murder.
It is Tiresias who killed Laius
Now I'm mad and I think that Creon killed him.
No, It was King Opedius
Queen Jocasta calms him down by telling him the prophecy of how their son would kill their father and marry his mother, Oedipus explains how he had the same prophecy, and also how he fought a man coming to Thebes.
I left Corinth to escape the same prophecy
We left our son in the woods to die because of a prophecy
But I did fight a man on my way here
A messenger comes to Thebes from Corinth, talking about how Oedipus' adopted father died of old age. This makes Oedipus think the prophecy is false, but then the messenger speaks of how Oedipus was abandoned but then saved.
Oedipus, your adopted father, the king of Corinth died of old age
You were abandoned but then saved
This proves the Prophecy is false!
Oedipus learns that the man he killed on his way to Thebes was his father, and that Queen Jocasta was his mother. this makes the prophecy true.
And your my mother!
I killed my father!
Please exile me!
Jocasta gets overwhelmed and hangs herself, Oedipus blinds himself and wishes to be exiled. But then Antigone and Ismene say that it will be decided by the gods.