Nothing is known of the Dragon God's history, other than that he was apparently worshipped by the dragons of the islands of Sostratos, before the dragons and many of its human inhabitants were wiped out by Hippolyta and the Amazons several centuries before the setting of the story, due to the piratical nature of the island's human inhabitants.
He has two known physical forms, one of a giant reptile-like creature, and the other being a man in gladitorial-like armour (suggesting that he may have simply been a disguise for Ares).
Long after the extermination of the dragons on Solstratos, the Dragon God suddenly reappeared to the battle's sole survivor, who was the only one left to bury the dead, and who had been in a state of constant grief and anger since the battle.
Knowing that this one dragon was not strong enough to defeat all of the amazons on its own, the Dragon God told it where it could find Hippolyta's daughter Diana (Wonder Woman), and he thus sent the dragon after her.
The dragon went to the city where Diana was staying, and caused chaos, death, and destruction, with untold casualties. When Wonder Woman was forced to fight it, it told her about the Dragon God, and she told it that the Dragon God was not real, that he was a trickster of some kind, and she tried to make peace with the dragon, but in the end was forced to kill it.
After Wonder Woman had buried the dragon in a human graveyard, she pledged to find the man who had sent him on the path of blood, whoever he (the Dragon God) really is.