Read The Great Books

Sophocles is one of three ancient Greek tragedians whose plays have survived (the other two being Aeschylus and Euripides). While Sophocles wrote over a hundred and twenty plays during the course of his life, only seven have survived in a complete form: Oedipus Rex, Oedipus at Colonus, Antigone, Philoctetes, Ajax, Elektra, and Women of Trachis.

The first set of plays recommended are the famous "Theban plays" consisting of three plays: Oedipus Rex, Oedipus at Colonus, and Antigone. All three plays concern the fate of Thebes during and after the reign of King Oedipus (where we get the "Oedipus Complex" from). It should be noted though that they are not really a trilogy; they do not form a continuous narrative and it is believed that they were part of other series of plays, which are now lost to time.

Philoctetes retells the story of Philoctetes, an archer abandoned on Lemnos by the rest of the Greek fleet on their way to Troy, who is then called upon again after the Greeks realize they cannot win the Trojan War without his bow.

Ajax focuses on Telamonian Ajax, the proud hero of the Trojan War, who is driven to treachery and eventually suicide.

1 The Complete Plays of Sophocles by Robert Bagg and James Scully is one of the best translations of Sophocles available. As a plus, you get all the plays of Sophocles (i.e., including Elektra and Women of Trachis).

Other famous translations of the Theban plays are the 2 Fitts and Fitzgerald one, and the 3 Robert Fagles version from Penguin. You could combine these with the 4 Meineck and Woodruff translations of Philoctetes and Ajax from Hackett.

To get more background on Greek (and Roman) theatre in general, a highly-recommended book is 5 The Cambridge Companion to Greek and Roman Theatre, which is a series of essays by prominent academics and practitioners investigating in detail the history of performance in the classical Greek and Roman world.