What is the history of the greek god Zeus?
First, I'm not sure if "history" is the right word here, since we don't really have any historical proof that Zeus existed. As for the mythic tradition surrounding Zeus, we can say plenty about that.
Zeus was one of six children of Cronus and Rhea. His father Cronus swallowed Zeus' other five brothers and sisters, but Zeus escaped that fate when his mother Rhea gave Cronus a stone wrapped in swaddling clothes instead. Zeus himself was smuggled away to the island of Crete and hidden until he grew, returned to Cronus, and tricked him into drinking a potion that caused Cronus to vomit up Zeus' brothers and sisters.
After this, Zeus and company waged war against Cronus. This battle became known as the Titanomachy. Eventually, Zeus and company defeated Cronus and his allies and banished them to the underworld. Zeus then became ruler of the gods and the sky, in particular.
Zeus also battled successfully against the monster Typhon and eventually led the other gods to victory against the Giants.
Zeus married his sister Hera, but he had numerous sexual affairs with both divinities and mortals and thus produced countless children. He was the father of several of the other leading divinities (e.g., Apollo, Athene, Artemis, Hermes, Ares, Dionysus) and many heroes (e.g., Heracles).
His most famous oracle in Greece was located at Dodona and his most famous cult-site in Greece was at Olympia, original home of the Olympic games. The people of Nemea also held some well-known games in his honor.
The poet of the twenty-third Homeric Hymn sings of his wisdom:
I will sing of Zeus, chiefest among the gods and greatest, all-seeing, the lord of all, the fulfiller who whispers words of wisdom to Themis as she sits leaning towards him. Be gracious, all-seeing Son of Cronos, most excellent and great! (Translation H.G. Evelyn-White)