To really see Clytemnestra in her element, you should turn to Agamemnon, the first play in Aeschylus's Oresteia trilogy. (You can also read all about her involvement in that play in our Shmoop guide.) Still, Clytemnestra plays a very important role in Libation Bearers as well, especially in her final dialogue with Orestes. The first actions Clytemnestra performs in Libation Bearers happen offstage: we only hear about them from other characters. The most important of these is the dream she has the night before the action of the play begins. In it, she dreams that she gives birth to a snake that drinks her blood along with her milk.
Clytemnestra shows her intelligence in interpreting the dream to mean some trouble from Orestes. She is also right in interpreting this trouble to be connected with Orestes's anger at the death of Agamemnon – causing her to send the libation bearers to Agamemnon's tomb. Sending the offerings to the tomb also shows us Clytemnestra's shamelessness, and determination to stop at nothing in order to save herself. Like, come on: you killed the guy, now you think some offerings of wine and water and stuff are going to set things right?
We first see Clytemnestra in person when Orestes and Pylades appear at the palace of Argos disguised as Parnassian travelers. You could say that both parties are in disguise: Clytemnestra's seeming grief at her son's death is what we'd expect from a mother – but we know that her real feelings are a little bit different. Clytemnestra also puts up a front of being a traditional female – as when she tells Orestes that he'd better talk to the men of the house if he has any serious business to attend to. But we know from Agamemnon that Clytemnestra is as good as any man in dealing with serious business, and she isn't what you'd call a traditional, conservative lady. Thus, this first appearance onstage really just reveals more of Clytemnestra's trickery.
Clytemnestra's intelligence and survival instincts are also on display when she instantly pieces together the cries of the House-Slave to realize that Orestes has killed Aegisthus. Her reaction? To demand that someone bring her a battle-axe. In the final confrontation, however, her wits are on display more than her skill with weaponry. Part of what she says and does is pure manipulation, as when she gestures toward her breast and asks how Orestes could possibly bear to injure the breast he nursed at. We know from the Nurse, however, that Orestes did not drink his mother's milk.
When Clytemnestra points out that Agamemnon had his own extramarital affairs, she finally elicits a little sympathy (from modern audiences at least). She cites the loneliness of wives sitting at home while their husbands are away at war – for 10 years, no less. Let us also not forget that Agamemnon made a human sacrifice of he and Clytemnestra's daughter, Iphigenia, just before heading off to Troy. He really was a long cry from father/husband of the year. Even when all hope is lost, Clytemnestra won't go down without a fight: she calls upon the Furies to avenge her and drive her son mad. Even in death, she has the power to hurt.