You were essentially, as Ketchup said, born one. As you/your character got older, your power became stronger and more evident to those who were sensitve enough to realize what you truely were.
What? I'm pretty sure it was the shattering of the worldstone that unlocked all those mighty abilities. In essence, I believe anyone could be nephalem, under the right circumstances... Wasn't it Uldyssian that, under Lilya's (sp?) influence, could awaken the latent nephalem powers on simple humans?