Oedipus Rex by Sophocles is considered to be one of the best tragedies every written. It chronicles a very short period of Oedipus's current life; most of the tragedy centers around what happened before the play begins and what happens after he finds out the truth about his past.
As the play opens, the priest and the citizens of Thebes have come to the royal palace to beg their king, Oedipus, to do something to alleviate their serious problems.
For our city, as you yourself can see,
is badly shaken—she cannot raise her head
above the depths of so much surging death.
Disease infects fruit blossoms in our land,
disease infects our herds of grazing cattle,
makes women in labour lose their children.
And deadly pestilence, that fiery god,
swoops down to blast the city, emptying
the House of Cadmus, and fills black Hades
with groans and howls.
The king listens, assuring them he has already taken action on their behalf by sending Creon to the Oracle of Apollo at Delphi.
The inciting action, the incident which changes the course of the play, happens early. One could make the case that it is when Creon returns from his task and announces what the Oracle told him: the city is harboring a the murderer of Laius, the former king of Thebes. One might also make the case that the inciting action is shortly after that, when Oedipus actually takes some action toward discovering the culprit; however, it seems to me that Creon's news is the spark that triggers the rest of the action. In either case, it is when Oedipus learns how he can lift the curse on his city that everything changes.
Rising action includes everything which leads up to the climactic grand revelation, and it begins with Oedipus asking questions about the death of Laius and his vow to discover the truth. He delivers his curses to those who have anything to do with the murderer (which of course is him) and sends for the blind prophet Teiresias. The prophet tells Oedipus the truth, though of course it is in veiled language, but the king does not believe him. In fact, Oedipus then accuses Teiresias and Creon of trying to usurp his throne and sends the prophet away. Creon and Oedipus argue, and Jocasta comes out of the palace to stop the fight. She tells the story of her own experience with prophecies which were not accurate (which, of course, we discover were actually true), and Oedipus gradually begins to suspect that he is the murderer of Laius. A messenger announces that Polybus is dead; a witness tells what he knows about the death of Laius and a shepherd admits he did not kill Jocasta's son as he was ordered to do. Jocasta realizes the truth and immediately goes inside and hangs herself.
In the tragic climax of this story, Oedipus also realizes the truth. (A case might also be made that Jocasta's death is actually the climax, since that is when the audience discovers the truth and Oedipus is simply slow to comprehend what he does not want to believe.)
The falling action is almost negligible. Oedipus goes inside and blinds himself because, he says,
In my wretched life, why should I have eyes
when nothing I could see would bring me joy?
The resolution/denouement is Oedipus's appeal to Creon to "see" his daughters for one last time and for Creon to banish him from the city. Creon agrees to both requests.