Native American Beliefs

The thing about this is our beliefs and religions are so closely tied to our languages, stories, and cultures that taking them out of those would make them pretty much useless. The best way to learn would be to find an elder, a medicine person, and ask them to mentor you.

This way you are getting permission from elders and you are not gobbling up all the crud on "shamanism" out there. Be prepared to be told no though, as many wont teach those outside of the tribe. If you did happen to find one, be prepared to learn language and culture of the tribe. It wont be easy.

Hey there. Although I'm not Native American, I do love the whatever I do know of their culture (which isn't much). I'm a tarot reader who uses the Medicine cards (http://www.medicinecards.com/). The handbook has interesting bits of stories behind almost every spirit animal. It is through learning to use it and learning about other people's experience from it that I've come to love the philosophy behind it.
This is all I know though (and it probably doesn't come close to the essence of their culture)... The rest involves fictional books :P

So I 100% agree with what's been said but I do recommend you Google a lot. Loto of.tribe's have closed communitys-yes. But also there's plenty of information out there from some how are open.
The only thing I feel a need to say (bc it's 99.99% completly inaccurate when non-natives use the term)- Spirit Animals. They are not meant to be your friend or even remotely like you. They fuck your shit up, make you uncomfortable in order for you to grow into the person you are meant to be and I haven't seen a single non-native book or teaching that actually understands that. It's going to be hard for you to find a real teacher as is- but I guarantee if you unknowingly give out the stereotype incorrect information on that your small pool of potential teachers will cut itself in half in outrage, disgust and/or offense. So be cautious what information you have, because it is probably wrong. Otherwise- start researching tribes and talking to people. Also I'm pretty sure there's tribes out in Europe (like the Sami tribe), why not look into them?

Syllabus, I wanted to thank you for your comment regarding spirit animals. As a member of the Blackfoot tribe, I have been upset seeing people group familiars with spirit animals.

To the original poster. Most of the information that has been provided is accurate. While no permission is needed from the tribe, it might be hard to get information from someone unless you are close friends. I also would urge you to wait for an invitation to a pow wow before going to one.