How were the dragons created? Did some God create them?
For example, we know that Melkor created the Dragons in Arda.
Is there something similar in the world of George Martin's?
Out of the original 3 dragons of the Targaryen conquerors, only Balerion came from Valyria. Meraxes and Vhagar were born on Dragonstone.
Other than that there is no information or "talk" on the origins of dragons. While they are connected to magic and seen as magical, they're also seen as animals. The people of Westeros don't discuss the origin of "cows" or "lions".
Everything about Valyria and its fall seems - even in universe - to be shrouded in myth and legend; as such we know very little about it.
AFAIK - and I've read pretty much everything connected to ASOIAF - Valyria in general has been mentioned only indirectly, and the origin of dragons hasn't been touched on at all.
Once there were two moons in the sky, but one wandered too close to the sun and cracked from the heat. A thousand thousand dragons poured forth, and drank the fire of the sun. That is why dragons breathe flame. One day the other moon will kiss the sun too, and then it will crack and the dragons will return. -- GOT page 235
It is known.
Here are some quotes from the books themselves:
She had heard that the first dragons had come from the east, from the Shadow Lands beyond Asshai and the islands of the Jade Sea. Perhaps some were still living there, in realms strange and wild. (A Game of Thrones, Daenerys III)
“Firewyrms. Some say they are akin to dragons, for wyrms breathe fire too. Instead of soaring through the sky, they bore through stone and soil. If the old tales can be believed, there were wyrms amongst the Fourteen Flames even before the dragons came. The young ones are no larger than that skinny arm of yours, but they can grow to monstrous size and have no love for men.” (A Feast for Crows, Arya II)
The Game of Thrones season 1 featurette "Valyria and the Dragons" confirms that the Valyrians did find dragons in the Fourteen Flames, though I'm not sure if it is really considered canonical.
Here's what we have from The World of Ice and Fire:
The Rise of valyria...
In such fragments of Barth’s Unnatural History as remain, the septon appears to have considered various legends examining the origins of dragons and how they came to be controlled by the Valyrians. The Valyrians themselves claimed that dragons sprang forth as the children of the Fourteen Flames, while in Qarth the tales state that there was once a second moon in the sky. One day this moon was scalded by the sun and cracked like an egg, and a million dragons poured forth. In Asshai, the tales are many and confused, but certain texts—all impossibly ancient—claim that dragons first came from the Shadow, a place where all of our learning fails us. These Asshai’i histories say that a people so ancient they had no name first tamed dragons in the Shadow and brought them to Valyria, teaching the Valyrians their arts before departing from the annals.
Yet if men in the Shadow had tamed dragons first, why did they not conquer as the Valyrians did? It seems likelier that the Valyrian tale is the truest. But there were dragons in Westeros, once, long before the Targaryens came, as our own legends and histories tell us. If dragons did first spring from the Fourteen Flames, they must have been spread across much of the known world before they were tamed. And, in fact, there is evidence for this, as dragon bones have been found as far north as Ib, and even in the jungles of Sothoryos. But the Valyrians harnessed and subjugated them as no one else could.
-The World of Ice and Fire, The Rise of Valyria.