Aristotle’s “Poetics” was intended as an analysis of the patterns of ancient Greek tragedy. Because Aristotle was attempting to explain how the major tragedies achieved their effects, he includes in his work extended analysis of several Sophoclean works, including Oedipus Rex, which he considered one of the best and most paradigmatic tragedies.
You can do an Aristotelian analysis of “Oedipus Rex” by reading through the play and looking for such standard elements as unities of time, place, and action. Think about the chain of choices which lead Oedipus to stray (“hamartein”), or make an irrevocable mistake. Also look of moments of recognition and reversal, and the ways in which the play can be said to purify its audience through fear and pity.