Zeus lay with Metis, the goddess of thought, but immediately feared the consequences. It had been prophesised that Metis would bear children more powerful than Zeus himself. In order to forestall these dire consequences, Zeus swallowed Metis immediately after laying with her. He was already too late: Metis immediately conceived a child. While the exact circumstances are unclear, shortly afterwards either Prometheus, Hephaestus, Hermes or Palamoan (depending on the sources examined) cleaved Zeus's head with an axe at the the river Triton. Athena leaped from Zeus's head, fully armed, and Zeus was none the worse for the experience.
Athena was patron of the crafts, wisdom and battle. Unlike Ares, who was hot-headed in battle (as well as cowardly), Athena's domain was strategy and tactics. She took the side of the Greeks in the war against Troy. Following the Trojan war, Athena assisted Odysseus on his journey home, for Odysseus had angered Poseidon, god of the sea, by blinding his son, Polyphemus the Cyclops.
Both the Trojan war and the journey of Odysseus are recounted by the Greek writer Homer in two epic poems, the Iliad (Ilion being the ancient name for Troy) and the Odyssey. (Available in Penguin classics among others, and a very good read.)
Athena became the patron goddess of the city of Athens, in a competition with Poseidon. Poseidon offered the Athenians a pool of salt, whereas Athena offered them an olive tree. The Athenians accepted the olive tree and along with it Athena as their patron. This is thought to remember a clash between the inhabitants during Mycenaean times and newer immigrants. It is interesting to note that Athens at its height was a significant sea power, at one point defeating the Persian fleet at Salamis in a sea battle. Athena was also the patron goddess of several other cities, notably Sparta.
Athena is usually portrayed wearing full armor and a shield, and carrying a lance. It is in this posture that she was depicted in Phidias's famous golden statue of her, now lost to history, in the Parthenon on the Athenian Acropolis.
Athena is also often depicted with an owl (a symbol of wisdom) sitting on one of her shoulders. It is interesting to note that while Homer's epithet for Athena is usually translated "owl-eyed", is can also be translated as "grey-eyed" or "wise-eyed".