I’ve talked about this here, but I might as well lay out the evidence:

Sheltered there, amidst the great volcanic mountains known as the Fourteen Flames, were the Valyrians, who learned to tame dragons and make them the most fearsome weapon of war that the world ever saw. The tales the Valyrians told of themselves claimed they were descended from dragons and were kin to the ones they now controlled…

The great beauty of the Valyrians—with their hair of palest silver or gold and eyes in shades of purple not found amongst any other peoples of the world—is well-known, and often held up as proof that the Valyrians are not entirely of the same blood as other men. Yet there are maesters who point out that, by careful breeding of animals, one can achieve a desirable result, and that populations in isolation can often show quite remarkable variations from what might be regarded as common. This may be a likelier answer to the mystery of the Valyrian origins although it does not explain the affinity with dragons that those with the blood of Valyria clearly had. (WOIAF)

“T///in the deep mines beneath the Fourteen Flames that lit the Freehold’s nights of old. Most mines are dank and chilly places, cut from cold dead stone, but the Fourteen Flames were living mountains with veins of molten rock and hearts of fire. So the mines of old Valyria were always hot, and they grew hotter as the shafts were driven deeper, ever deeper. The slaves toiled in an oven. The rocks around them were too hot to touch. The air stank of brimstone and would sear their lungs as they breathed it. The soles of their feet would burn and blister, even through the thickest sandals. Sometimes, when they broke through a wall in search of gold, they would find steam instead, or boiling water, or molten rock. Certain shafts were cut so low that the slaves could not stand upright, but had to crawl or bend. And there were wyrms in that red darkness too…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.” (AFFC)

“In Septon Barth’s Dragons, Wyrms, and Wyverns , he speculated that the bloodmages of Valyria used wyvern stock to create dragons. Though the bloodmages were alleged to have experimented mightily with their unnatural arts, this claim is considered far-fetched by most maesters, among them Maester Vanyon’s Against the Unnatural contains certain proofs of dragons having existed in Westeros even in the earliest of days, before Valyria rose to be a power.” (WOIAF)

So the theory is that Valyrian sorcerors knew fire magic and blood magic, and created dragons by unnaturally crossbreeding firewyrms and wyverns together, and then learned to form bonds with dragons by unnaturally crossbreeding dragons and Valyrians together.