Oedipus came to be King of Thebes when he solved the riddle of the Sphinx...
and released Thebes from her tyranny. (In ancient Greece, the Sphinx had the body of a winged lioness and the head of a woman. The Egyptian Sphinx had, and has, the body of a lion and the head of a man.) In addition to being made King, Oedipus was also given the hand of the former Queen,Jocasta, in marriage. Oedipus knows that he's King only through a twist of fate and as the result of a remarkable series of events.
From all appearances, Oedipus is a benevolent king, and the people of Thebes revere and respect him. The Priest refers to Oedipus as "our peerless king." Oedipus repeatedly refers to his people as "my children."
In the opening scene of the play, Oedipus commiserates with the supplicants who have come to his palace, and he grieves with them for the drought and plague that has befallen them. His sympathetic words to the Theban people seem genuine and heartfelt. He rules by mutual love and mutual respect. He doesn't need to prove to anybody that he's the King, and he rules with a light touch.
However, Oedipus is arrogant:
OEDIPUS: Children, it were not meet that I should learnFrom others, and am hither come, myself,I Oedipus, your world-renowned king.
Oedipus is also headstrong and prideful. Until it's proven to him absolutely and without any reasonable doubt that he's the murderer of Laius, the previous King of Thebes and his own father, and that he married his own mother, Jocasta, it's entirely reasonable that Oedipus refuses to believe something that is frankly so unbelievable.
As the plot moves forward and evidence mounts up against him, Oedipus becomes increasingly isolated and increasingly unreasonable, and he lashes out at everyone around him. He accuses Teiresias of lying to him. He also accuses Creon and Teiresias of conspiring to usurp his throne.
This is when Oedipus brings his power to bear in a negative way. Although Oedipus makes no threats against Teiresias earlier in the play, even when Teiresias reveals the Oedipus is the murderer of Laius and has married his own mother, Oedipus now threatens Creon with a public death when he thinks that Creon is plotting to overthrow him.
CREON: What then's thy will? To banish me the land?
OEDIPUS:I would not have thee banished, no, but dead,That men may mark the wages envy reaps.
Jocasta appears from inside the palace and tells the story of how she and Laius tried to save their son from the prophecy that he would kill his father and marry his mother. The Herdsman is brought in to tell the story of how he saved Oedipus from death. As the pieces of the Oedipus puzzle fall into place, Oedipus realizes that, even through no fault of his own, he's defied the gods and brought destruction to himself and his family.
At this point, Oedipus does the right thing, peacefully relinquishes his power to Creon, and banishes himself from Thebes.
Unfortunately, Creon makes a right mess of things in Antigone, but that's another story.