Zeus is the son of Cronus. Cronus was the king of the Titans, god of time and the ages(he presided over the Golden Age) and his sister, Rhea, was queen. Cronus received a prophecy stating that he would be overthrown by his son just as his father, Uranus, was overthrown (castrated) by him. To avoid this, he swallowed each of his children immediately after their births: Hestia, Demeter, Hera, Hades, Poseidon, and lastly Zeus who was not eaten. Rhea tricked Cronus by wrapping a stone in blankets to make Cronus think it was the baby Zeus. When Zeus was old enough and strong enough, he called on his uncles, Cronus' brothers, the cyclopses, whom Cronus had imprisoned. Zeus defeated the Titans along with his brothers and sisters who were freed from Cronus' belly, and they were all cast into Tartarus, the worst level of Hades. Before Cronus was locked away he cursed Zeus, as his father had done to him, to bare the same fate as to be overthrown by his own son. The brothers (Hades, Poseidon, and Zeus) "drew straws" to see who would inherit which kingdom: Zeus got the heavens, Poseidon got the sea, and Hades got the underworld. After his victory, Prometheus warned him about bedding Thetis because a child born by her would be greater than his father and so Zeus took Metis (goddess of wisdom) as his first wife. Unfortunately for her he received a prophecy that Metis' child would be the wisest of the gods and so he swallowed her, baby and all. After swallowing her, he inherited her wisdom and so also became the god of wisdom and law and order (thanks to Themis and her daughters) and so was called also The Wisest Councellor. Of course from Zeus' head sprang the fully-formed Athena who also became the goddess of wisdom, but only wisdom in battle.
Because Zeus is a sky god he is known also as The Cloud-Gatherer, The Thunderer, etc. When he shakes his aegis it produces the storm and tempest. After his wife Hera birthed Hephaestus, the smith god, he made Zeus his legendary thunder bolts.
Prometheus is the Titan god of forethought (he's not really a titan though, only the son of one), his brother (in some myths his son) Epimetheus, is the god of after-thought. Pometheus is most often associated with fire or the torch because of his gift to man. He is called the father of man, while his brother, After-thought, is supposed to be the father of woman. Prometheus was responsible for molding mankind out of clay. He created the men of the Golden Age, but because Gaie provided all that they needed, they had no use for fire. Fruit grew itself and the rivers streamed with milk and honey (some myths say ambrosia), animals were not hunted (they could talk!) and there was only one season, Spring, so there was never any cold. Man lived beneath the sun and slept beneath the stars. When Zeus took over he ushered in a new race, the men of the Silver Age. Along with this new age came new seasons. People had to sleep in caves to avoid the harsh elements. Fruit no longer grew year round and so they had to hunt. Animals turned their backs from men and so could no longer speak with them. Prometheus wanted to protect his creation; he saw that, without fire, man-kind would not survive and so he stole it from Zeus and took it to them. Zeus was angry because of Prometheus' trick and so he imprisioned him on Mount Kaukasos and ordered an eagle to visit him during the day to eat his liver. Because Prometheus was immortal he could not die and so his liver would regenerate each night only to be eaten again the next day! For man, Zeus punished them by creating Pandora and gifting her with the box that contained every evil and wicked thing, along with hope. Pandora opened the box and so ushered in the next age, the Bronze Age. It was after the Bronze Age that King Lycaon offended Zeus and Zeus flooded the Earth that man was remolded by Deucalion and Phyrra with the help of Themis out of stone and so became cold and hard and the last age was ushered in, The Iron Age. Some myths state that there was an age in between the two called the Hero Age where the gods went through a raping-spree, but it is sometimes simply lumped in with the Bronze Age.
If you really want to start getting into Greek myth you can read Edith Hamilton's Mythology or take a look at Ovid's Metamorphosis. They're both great reads, but Hamilton's is a little easier on beginners.