I have a copy of Native North America by Larry J. Zimmerman and Brian Leigh Molyneaux (University of Oklahoma press). It has a section on Sacred History (creation stories, culture heroes) spirituality in the ''present'' or at least in 1996 when the book was written (that section includes the significance of dreams, dances, and drum circles).
The thing is, continental America is a really big place. Huge. Even if you limit your region to North America as in the United States, or North America as in Canada, or even Meso-America like the spirituality of Aztec civilization, the inhabitants before colonialism did everything very differently depending on which group they were in.
Michael Harner wrote a book about Core Shamanism. The word ''shamanism'' was used by anthropologists to generalize spiritual traditions, and it's popular and influential among New Agers, especially in America where there would be the cultural diffusion going on. The term has become outdated because it doesn't actually describe a tradition, but it might be closer to what you're looking for.