More of a personal perspective on Native spirituality:
The info on native religion was rather dry, so here, now is my experience and impression of it where I’m from.
Natives here tend to quietly practice. They will hold ceremonies for the public occasionally, but mostly, they practice for themselves. They can be mistrustful of “outsiders” showing interest in their practices for fear of ridicule or being treated as novelties. Anyone, generally can however attend many of the ceremonies.
Tribes have Elders who will advise on spiritual and general matters. They will also see outsiders if the outsider seems sincere. Natives do not view themselves as the chosen ones, and anyone can follow their ways. Of course, race and culture can cause tension.
There are many who mix christianity with native spirituality, and it really depends on the person’s background as to what is emphasized. With me, for example, our home was strict catholic (due to my mother) with my agnostic dad influencing us indirectly to question. My maternal grandfather (native) didn’t preach (he was married to a staunch catholic) but would take me into the woods with him to check his trap lines, to fix fences, to hunt, etc. From him I received a different view of the world, how we don’t own it, but are allowed to use it as is any other living and non-living thing. We are responsible for damage we cause to the world, and while allowed to hunt and trap, should show respect for what is taken.
He would do these little rituals like mumbling to the animal he had killed, disposing of the body in certain ways (laying a bird in tree branches, burning in a pyre made for that purpose, etc., but wouldn’t explain unless I asked, then he’d keep it vague, out of respect (or fear! ) of his catholic wife. Just walking through the woods with him was a spiritual event. It was how he treated everything with respect and as though everything had consciousness, spirit. While we never practised native religion, weren’t even taught it, his actions, and those of my uncle, had impact on some of us. We would tend to make up our own ways, combining catholicism and native spirituality. Another example - despite having my fingers rapped by nuns repeatedly, I continued to believe everything has spirit.
Remember, these are my experiences, and I don’t claim they are true for all natives and métis.
For literature, Black Elk Speaks: Being the Life Story of a Holy Man of the Oglala Sioux Black Elk witnessed the Battle of Little Bighorn in 1876 and the upheaval that followed the tribe's flight to Canada to join Sitting Bull. In this book, he describes his childhood and early adult life and the spiritual life of the Sioux.
Here is the link to the text; the site has other native writing as well.