Exposition generally occurs at the start of a story. Exposition is used by an author to reveal the setting, characters, and conflicts of a story. In Oedipus the King, or Oedipus Rex, Sophocles uses lines 1 through 774, up until we first meet Jocasta, to set up the exposition. Through the exposition, we learn the story is set in Thebes and the central conflict is that Thebes is being ravished with plague; Oedipus's brother-in-law, Creon, has returned from consulting the Oracle of Delphi to report that the plague is a consequence of the city still harboring the murderer of King Laius, Jocasta's late husband.
Authors create plot complications by adding new twists to the conflict that make the story more suspenseful. Sophocles' plot complication occurs the moment King Oedipus vows to find King Laius's killer and asks for anyone with information to step forward, only to be told by the soothsayer Teiresias that Oedipus himself is the "accursed polluter of this land" (421) and to say how completely blind Oedipus is to the extent of damage his own arrogance and hotheaded temper have caused:
[Y]ou have your eyesight, and you do not see how miserable you are, or where you live, or who it is who shares your household. (496-98)
The climax is defined as the turning point in the story, the moment when rising action turns to falling action, leading towards the resolution. The climax is also often the most emotionally intense moment of the story. The climax occurs soon after the messenger from Corinth comes to announce the death of Oedipus's father, King Polybus, and further informs Oedipus that Polybus and Merobe were really Oedipus's adopted father and mother. Soon after this, the shepherd is sent for who had given baby Oedipus to the messenger. The climax occurs the moment the shepherd confesses to having saved the life of baby Oedipus, King Laius's son, by giving him away; the shepherd's confession, coupled with the scars on Oedipus's ankles, proves that Oedipus was the son of King Laius, the father he had killed at the crossroads near Delphi.
The denouement is defined as the continuation of the story after the resolution, bringing the story to an end. The resolution occurs the moment Oedipus realizes the extent of the damage he has caused since he truly did kill his own father, fulfilling the prophecies. The details of the denouement include his gouging out his own eyes to symbolize that Teiresias was correct to have called him blind, Jocasta hanging herself, and Oedipus saying goodbye to his children before being led out of the city in exile.
The exposition of Sophocles' Oedipus the King occurs in a fairly organic way in this play. The audience learns from conversations that Oedipus has with the Priest and Creon that the plague afflicting the Thebans is caused by the continued presence of Laius' killer within the city.
The play's complication, I would say, occurs when Teiresias arrives and is goaded into telling Oedipus that he is the person who killed Laius and who married his mother.
The climax takes place when Oedipus learns from the Theban shepherd that Jocasta had given the baby Oedipus to him to expose on Mount Cithaeron, but that the Theban shepherd gave the baby to the Corinthian shepherd, who in turn gave Oedipus to Polybus and Merope of Corinth. Oedipus responds:
Ah, so it all came true. It’s so clear now.
O light, let me look at you one final time,
a man who stands revealed as cursed by birth,
cursed by my own family, and cursed
by murder where I should not kill.
(Ian Johnston translation)
The denoument in this tragedy occurs at the play's conclusion. Oedipus, having learned that the prophecies about him have come true, has blinded himself. Having blinded himself, Oedipus laments his fate, pleads with Creon to banish him, but also does not want to be parted from his children. The play ends with the chorus commenting on how a person's fortunes can change in an instant.