How did animism spread?

A:

Animism did not spread so much as arise spontaneously in different places. Religion has always been a way to explain that which we do not understand, and a way to help control the elements of nature.

Every region had its own sacred stories and its own spirits. The elements common to animism in different regions are those elements that could reasonably have arisen in parallel. Perhaps different regions influenced each other, but any interaction between, for example, Eurasian and American animists must have occurred before the migration across the Bering Strait.