Each had their own different creation idea. Within ancient Greece, the commonly accepted idea stems from Hesiod's Theogony 116-159 which tells the formation of the world as they knew it.

Chaos started it all and produces Eros (love/sexual desire), Erebos (death/darkness) and Night (night itself)

Then came the Earth (Gaia) which covers everything in the world including Olympus (place of Gods) and Tartarus (underworld).

Earth and Heaven then combined to produce several other things such as the Cyclopes, 100-handed, 50-headed sons and then physical things such as the sea, hills, ocean and then both Rhea and Cronos.

Cronos then attacks Heaven and cuts off his genitals with a sickle. Heaven’s blood then combines with the Earth to produce the Erinyes and Giants and with the Sea to produce Aphrodite (god of love) as well as the Titans.

Cronos then has children with Rhea but eats them to avoid them doing what he did to his father. Rhea though tricks Cronos by replacing Zeus with a stone and raising him elsewhere. Zeus then challenges Cronos and defeats him and takes over as the king of Gods with Cronos vomiting up his previous children.

Zeus also brings up the Titans and others (100 handed 50 headed sons) and engages in a battle with them, overcoming them. He also overcomes Typhoeus and remains in power. This also gives the story of how the Gods came to their current power.

For actual mankind it was thought that Prometheus was the creator. It was said that he molded man out of mud and then Athena breathed life into the mud and man was given life. It was then said that Zeus had men make sacrifice in the name of the gods and Prometheus tricked Zeus in accepting basically the rubbish part of the animals (bones+fat) over the meat. Zeus then took away fire but Prometheus stole it back and gave it back to man.

Zeus was not happy with this and created Pandora, the first woman, and with her opening of Pandora's box she released evil upon the world. Prometheus was also punished in the known myth.

There were several different views. Hesiod's Theogony is a very important source - the myth of the Four Ages was exceptionally influential. Here's a rather different view, to give you an idea of the variety.

Lucretius (latter half of the 1st century BCE) was a Roman poet and Epicurean philosopher. In Book 5 of his epic poem On the Nature of the Universe (De rerum natura), he writes that the earth in its infancy produce a kind of womb attached to the ground with roots, in which the different creatures developed. After birth, creatures would be nourished by a milk-like liquid welling up in that area. Some of the creatures were not well-adapted to life (lack of senses, lack of mobility, inability to breed etc.) and died out. Others survived either through their own strength, skill etc. or by being useful to humans.

As for human development, he writes:

And the race of men at that time was much hardier on the land as was fitting inasmuch as the hard earth had made it: it was built uo within bones larger an dmore solid, fitted iwth strong sinews throughout the flesh, not such as easily to be mastered by heat or cold or strange food or any ailment of the body. Through many lustres of the sun rolling through the sky they passed their lives after the wide-wandering fashion of wild beasts. No sturdy guider of the curved plough was there, none knew how to work the fields with iron, to dig new shoots into the ground, to prune off old branches from the tall trees with a sickle. What sun and rain had given, what the earth had produced of her own accord, that was a gift enough to content their minds. Amidst the acorn-laden oaks they refreshed themselves for the most part; and the arbute-berries, which in winter-time you now see ripen with crimson colour, then the earth bore in abundance and even larger than now. Many another kind of food besides the flowering infancy of the world thenproduced, hard by amply sufficient for poor mortals.

But to quench thirst, rivers and springs invited them, as now the rushing of water down from the great mountains calls loud and far to the thirsting tribes of beasts. Moreover, they dwelt in woodland precincts of the Nymphs, familiar to them in their wanderings, whence they knew that some running rivulet issued rippling over the wet rocks, rippling over the wet rocks in abundant flow and dripping upon the green moss, and in parts welling up and bubbling out over the level plain.

Not yet did they know how to work things with fire, nor to use skins and to clothe themselves in the strippings of wild beasts; but they dwelt in the woods and forests and mountain caves, and hid their rough bodies in the underwoods when they had to escape the beating of wind and rain.

They could not look to the common good, they did not know how to govern their intercourse by custom and law. Whatever prize fortune gave to each, that he farried off, every man taught to live and be strong for himself at his own will.

And Venus joined the bodies of lovers in the woods; for either the woman was attracted by mutual desire, or caught by the man's violent force and vehement lust, or by a bribe - acors and arbute-berries or choice pears.

And by the aid of their wonderful powers of hand and foot, they would hunt the woodland tribes of beasts with volleys of stones and ponderous clubs, overpowering many, shunning but a few in hiding-places.

And when night overtook them, like bristly hogs they just cast their savage bodies naked upon the ground, rolling themselves in leaves and boughs. Nor did they go seeking the day and the sun with great outcry over the countryside, wandering panic-stricken in the shadows of night, but waited quiet and buried in sleep until the sun with rosy torch spread his light over the heavens. For since they had been accustomed from childhood always to see darkness and light return in alternate sequence, it was impossible that they should ever feel wonder, or fear lest everlasting night should possess the world, the sun's light being withdrawn for ever. Rather what troubled them was that the tribe of beasts often made their rest dangerous to the poor wretches: driven from their home, they would flee from their rocky shelters when a foaming boar appeared or a mighty lion, and at dead of night in terror would yield their leaf-strewn beds to the savage guests.

Nor did mortal men much more then than now leave with lamentations the sweet light of life. True, each one was then more likely to be caught and devoured alive by wild beasts, torn by their teeth, and to fill woods and forests and mountains with groaning as he saw his own living flesh buried in a living tomb; while any that flight had saved with mangled body afterwards held their trembling hands over the hideous sores, calling on Orcus with horrible cries, until cruel torments put an end to their life, with none to help, all ignorant what a wound wanted. But one day did not send to destruction many thousands of men in the battle-field, ships and mariners were not dashed on the rocks by the turbulent bellows of the sea. Then it was all in vain, all useless, all for nothing that the sea often rose and stormed, and lightly it laid aside its threats without meaning, nor could anyone be enticed to his ruin by the treacherous witchery of a quiet sea with laughing waves. The wicked art of navigation then lay hidden and obscure. In those days again, it was lack of food that drove fainting bodies to death; now contrariwise it is the abundance that overwhelms them. In those days men often unwittingly poured poison for themselves, now they make away with themselves more skilfully.

Next, when they had got themselves huts and skins and fire, and woman mated with man moved into one [home and the laws of wedlock] became known, and they saw offspring born of them, then first the human race began to grow soft. For the fire saw ot it that their shivering bodies were less able to endure cold under the canopy of heaven, and Venus sapped their strength, and children easily broke their parents' proud spirit by coaxings. Then also neighbours began to join friendship amongst themselves in their eagerness to do no hurt and suffer no violence, and asked protection for their children and womankind, signifying by voice and gesture with stammering tongue that it was right for all to pity the weak. Nevertheless concord could not altogether be produced, but a good part, indeed the most, kept the covenant unblemished, or else the race of mankind would have been even then wholly destroyed, nor would birth and begetting have been able to prolong their posterity to the present day.

(Loeb translation. Square brackets indicate an emendation of a damaged line.)