Every locale had its stories of the gods, not in isolation but relative to the landscape and the people of old, perhaps heroes, that had lived in it. Greece does not bother much with creations and ends of the world, except at a sort of philosophical level. So Zeus is not a creator god. And indeed the Olympians are in mythology a relatively new regime: before them there had been the Titans, and at the beginning there was either Ocean (as in Homer) or Chaos (‘‘the Gap’’) - both of them probably Near Eastern imports. You read Hesiod’s Theogony for this back story of the gods, for a sense of where the present order of gods came from. And he may tell you in the Works and Days that we live in very fallen times, in the Age of Iron, but most Greeks, whilst admitting, as all traditional societies do, that values were enshrined in their elders and ancestors, thought mainly about the present, and it was in the present that Zeus and the Olympians ruled.
Simple books and web pages will list you the Olympians’ functions. Zeus is the king of the gods and the god of the sky. Hera is the goddess of marriage. Ares is the god of war. Poseidon is the god of the sea, and earthquakes. Demeter is the goddess of corn and fertility. Aphrodite is the goddess of sex. Artemis is the goddess of the hunt. Dionysus is the god of wine and madness. Apollo is the god of law and of order, music and literature, divination and oracles (but emphatically not god of the sun). Hestia is the goddess of the hearth. Hermes is the messenger god, and god of travelers and traders. Hephaestus is the god of smiths and in a sense of fire.
These are tidy roles for our principal gods and provide a way of understanding their community. Delightful use can be made of such roles by poets, as when the Iliad’s Aphrodite is wounded for being so foolish as to partake in battle (5.428), and its Ares, because he personifies the evil of war, is loathed by other characters. Apollo can decline to take part in a battle because he has a superior mentality and is more acutely conscious of the special status of god relative to man (Iliad 21.461-7).
And this is a tradition which continues, especially in lighter vein, to be exploited throughout antiquity and on into the medieval and modern European tradition. A particular source for the lighter approach is Ovid’s wickedly ingenious Roman epic, the Metamorphoses (complete by AD 8), a work which was to become, as is sometimes said, the ‘‘bible’’ of European painting. Here Jupiter (Zeus) smites the wicked Lycaon, king of Arcadia, who tried to feed him human flesh, and turns him into a wolf. Apollo seeks to rape the nymph Daphne, but she can only turn into a laurel and be appropriated by him as his special tree. Jupiter falls in love with lo, but regrettably is obliged to transform her into a cow owing to the jealousy of his wife Juno (Hera). And he fares no better with Callisto, who is converted into a bear by Diana (Artemis) owing to her pregnancy. And then there are Semele and Danae: Semele tricked by Juno into making the fatal request that Jupiter should appear to her in his real form, the lightning; Danae locked in a tower only to be impregnated by Jupiter in the form of golden rain. These stories from the first few books of Ovid’s Metamorphoses have entranced us all and form that central core of what mythology means to us. But they are of course the tip of an iceberg and are themselves culturally transformed from local stories told for a reason into the rich symphony of classical culture.
From there this view continues strongly as Christianity supersedes the religious dimension of the pagan gods - thus what remains for the pagan gods is principally the decorative dimension, myth and its representation. So in European culture, particularly painting and opera, the gods are strongly functional and conventional. As a result, given that most of us come to Greek religion via Greek mythology, our perceptions are shaped by this view and almost all the basic books and web pages peddle this colorful and historically influential, if not very religious, view of ancient gods.