Athena was born a child of Zeus by his first wife, Metis, a goddess of wisdom. Because Zeus was afraid Metis might bear him a son who was mightier than himself, he swallowed her. While trapped inside Zeus, Metis began to make a helmet and robe for her unborn daughter. All that clanging and pounding caused Zeus to suffer terrible headaches, so he called for his son Hephaestus, the smith of the gods. Hephaestus split his father's skull open to relieve the pain, and out popped Athena, fully grown and clad in her new robe and helmet.
The cult of Athena emerged very early, as part of her position as a patroness of the city of Athens. She became Athens' protector after a dispute with her uncle, Poseideon, the god of the sea. Both Athena and Poseidon really liked a certain city on the coast of Greece, and both of them claimed ownership.
Finally, to solve the dispute, it was agreed that whoever could present the city with the best gift would forever be patron. Athena and Poseidon went to the Acropolis, where Poseidon struck the cliffside with his mighty trident. A spring welled up, which amazed and impressed the citizenry. However, the spring was salt water, so it wasn't really of much use to anyone.
Athena then presented the people with a simple olive tree. Although it wasn't as impressive as a spring, it was far more useful, because it presented the people with oil, food, and even wood. In thanks, they named the city Athens. Some people in Greece still worship Athena and pay homage to her at the Acropolis.
Athena is typically portrayed with her companion, Nike, the goddess of victory. She is also depicted carrying a shield bearing the head of the Gorgon. Because of her association with wisdom, Athena is usually shown with an owl nearby.
As a goddess of war, Athena often shows up in Greek legend to assist various heroes -- Heracles, Odysseus and Jason all got a helping hand from Athena. In classical myth, Athena never took any lovers, and was often revered as Athena the Virgin, or Athena Parthenos. This is where the Parthenon temple got its name. In some older stories, Athena is connected as either the mother or adoptive mother of Erichthonius, after an attempted rape by her brother, Hephaestus. In some versions of the story, she is a virgin mother, who raised Erichthonius after he was given to her by Gaia.
In another tradition, she is known as Pallas Athena, with Pallas actually being a separate entity. It's not clear whether Pallas is actually Athena's father, sister, or some other relationship. However, in each story, Athena goes into battle and accidentally kills Pallas, then taking the name for herself.
Although technically, Athena is a warrior goddess, she is not the same sort of war god that Ares is. While Ares goes to war with frenzy and chaos, Athena is the goddess who helps warriors make wise choices that will eventually lead to victory.
Today, many Hellenic Pagans still honor Athena in their rituals.