Disclaimer: Tolkien's the genius, not me.
As the world crumbled, Morgoth’s once-great lieutenant slunk away, heading eastward. For many years he wandered, passing through the great forests of Eriador and Rhovanion, without even a broken twig to mark his passing.
At last he came to a land walled by mountains, like broken teeth jutting into the sky. And the mountain of fire: the perfect forge where he would craft his most powerful weapons. It would take many decades in the count of Men and Elves to gather his forces and fortify this land properly, but Sauron was patient.
Eventually, he would succeed where Melkor had failed.