In Greek mythology, Cronus/Kronos and Gaea were the first gods to exist, Gaea the goddess to rule the Earth and Cronus the moon. When they first appeared, the Earth was already in existence. Neither Gaea nor Cronus have created the Earth and seemingly, the Earth was created by something or someone before them.
So how was the Earth created in Greek mythology?
First, there was nothing. Absolutely nothing.
Then,
In the beginning there was only Chaos. Then out of the void appeared Erebus, the unknowable place where death dwells, and Night. All else was empty, silent, endless, dark. Then, Love was born bringing along the beginning of order. From Love emerged Light, followed by Gaea, the earth.
http://www.greekmythology.com/Myths/The_Myths/The_Creation/the_creation.html
That's one version. Another explanation is
It all started when Chaos, Gaea (Earth) and Eros started sleeping with each other, leading to the Gods. So, in Greek mythology, the creation of the world starts with the creation of the different classes of Gods. In this instance, the term 'gods' refers to the characters that ruled the Earth (without necessarily possessing any divine attributes) until the 'real' Gods, the Olympians, came.
http://www.greekmythology.com/Myths/The_Myths/The_Creation_II/the_creation_ii.html
These are based in Hesiod's Theogony. I was able to find an actual quote from it:
Declare to me from the beginning, you Mousai who dwell in the house of Olympos, and tell me which of them first came to be.
In truth at first Khaos (Air) came to be, but next wide-bosomed Gaia (Earth), the ever-sure foundation of all the deathless ones who hold the peaks of snowy Olympos, and dim Tartaros (the Pit) in the depth of the wide-pathed Earth, and Eros (Love), fairest among the deathless gods, who unnerves the limbs and overcomes the mind and wise counsels of all gods and all men within them. From Khaos (Air) came forth Erebos (Darkness) and black Nyx (Night); but of Nyx (Night) were born Aither (Light) and Hemera (Day), whom she conceived and bore from union in love with Erebos. And Gaia (Earth) first bore starry Ouranos (Heaven), equal to herself, to cover her on every side, and to be an ever-sure abiding-place for the blessed gods. And she brought forth long Ourea (Mountains), graceful haunts of the goddess Nymphai who dwell amongst the glens of the hills. She bore also the fruitless deep with his raging swell, Pontos (Sea), without sweet union of love.
But afterwards he [Gaia, Earth] lay with Ouranos (Heaven) and bare deep-swirling Okeanos, Koios and Krios and Hyperion and Iapetos, Theia and Rhea, Themis and Mnemosyne and gold-crowned Phoibe and lovely Tethys. After them was born Kronos the wily.
-- Hesiod, Theogony 115
Aristophanes had a slightly different version:
At the beginning there was only Khaos (Air), Nyx (Night), dark Erebos (Darkness), and deep Tartaros (Hell's Pit). Ge (Earth), Aer (Air) and Ouranos (Heaven) had no existence. Firstly, black-winged Nyx (Night) laid a germless egg in the bosom of the infinite deeps of Erebos (Darkness), and from this, after the revolution of long ages, sprang the graceful Eros (Love) with his glittering golden wings, swift as the whirlwinds of the tempest. He mated in deep Tartaros (Hell-Pit) with dark Khaos (Air), winged like himself, and thus hatched forth our race [the birds], which was the first to see the light. That of the Immortals did not exist until Eros had brought together all the ingredients of the world, and from their marriage Ouranos (Heaven), Okeanos (Ocean), Ge (Earth) and the imperishable race of blessed gods (Theoi) sprang into being.
-- Aristophanes, Birds 685
In both cases, Gaea is understood to be a personification of the Earth; the same goes for Chaos, Erebus/Erebos, Eros, and many of the others.
For information on just how Gaea begat her children, see How were the first children of Gaia conceived?.
It's not made clear how the Earth was created. It just came to be, having been born after Chaos came into existence:
Citing Wikipedia:
Η Γαία (αρχ. ελλ.: Γαῖα) προϋπήρχε με το Χάος και τον Έρωτα-Φάνη στη δημιουργία του Κόσμου.
Earth pre-existed with Chaos and Eros (Love) in the creation of the world.
Citing Theogonia:
First of all Chawos [Gap] came into being. But then Gaia broadchested, always the unshakable seat of all the immortals who hold the peaks of snowy Olympus,and dark Tartaros in the recesses of the wide-wayed earth, and Eros, the most beautiful among the immortal gods, loosener of limbs, who subdues the mind and prudent counsel in the chests of all gods and of all men.
So, once can suggest, that Earth was a deity which pre-existed, without an explanation of how it came to be.
