Sophocles wrote "Oedipus the King" for the annual festival where playwrights competed for prizes. It was a major civic occasion, with attendance expected.
Sophocles the writer is phenomenally good, especially considering his era. His writing is tight, with each phrase contributing to the whole. He is full of succinct observations on life. And despite the limits of the form, he often manages to make his characters seem like real individuals.
The title of our play is often given in its Latin translation "Oedipus Rex", rather than in its original Greek ("Oedipus Tyranneus"), since the Greek term for king is the English "tyrant" which means a monarch who rules without the consent of the people.
As the play opens, the priest of Zeus and a bunch of non-speaking characters (old people, children) appear before King Oedipus with tree-branches wrapped with wool. It was evidently the custom to do this in front of a god's altar when you wanted something urgently.
Oedipus greets them as a caring, compassionate leader. The priest explains (really for the audience's benefit) that Thebes is suffering from a plague. Plants, animals, and people are all dying. The people know Oedipus is not a god, but they believe that some god inspired him to solve the riddle of the sphinx and save the town. And since Oedipus has been king, he has done a splendid job. So now people look to him to find a cure for the plague.
Oedipus explains (really for the audience's benefit) that he has sent Creon