This is a pretty broad question; there are literally hundreds of different native cultures within the United States alone, and hundreds more if you extend your search into the arctic regions and Central and South America. It’s a little like asking about “European” culture — France is different from Germany is different from Italy is different from Poland is different from Croatia… Or asking about “Chinese” culture — there are dozens of cultural groups within China itself, plus major ethnic Chinese cultures in other countries that have diverged from their origins.

That said, a good place to start is the National Museum of the American Indian (a part of the Smithsonian). It has lots of excellent free resources available online. There are also physical museums in New York City and Washington, DC.

There are also resources that are focused on more local or specific cultures and nations. For instance, the Six Nations Iroquois Cultural Center, or the Navajo Nation.

Are you interested in Mesoamerican art and artifacts too, or just ancient peoples of what is now the United States?

If so, I would recommend From the Olmecs to the Aztecs for a general overview of major Mesoamerican cultures and The Maya for a good overview on just the Maya, both by Michael D. Coe. Some good books just on art are The Gods and Symbols of Ancient Mexico and the Maya by Mary Miller and Karl Taube and The Art of Mesoamerica by Mary Miller.

1491: New Revelations of the Americas Before Columbus. by Charles C. Mann.

This is a great book by a non-anthropologist for lay people and professionals alike. It is a lengthy discussion of the diversity of new world cultures prior to European contact. It describes the current anthropological thinking on the original peopling of the Americas, the degree to which natives modified their environment, and the cultural richness of pre-contact America.

Facing East from Indian Country by Richter is a decent place to start for learning about some of the material culture of native peoples in North America.

Rising Up from Indian Country by Keating is also a good attempt at flipping the perspective on Fort Dearborn and the establishment of Chicago.

I think both of these are ok books, but keep in mind that they are still flipping the perspective but still with a pretty white academic point of view. Good places to start, but if you want to continue, you'll need to do some further reading.

Braiding Sweetgrass by Kimmerer is a recent memoir by a Potawatomie woman that discusses native folkways and merging them with modern science. This can really help you understand notions of nature, consumption, and private property.

Empire of the Summer Moon by Gwynne has a good narrative structure and I think gives an accurate feel for the reality of the Comanches in a certain era (and by extrapolation some other peoples). It breaks the incorrect notion that natives were all peaceful and naive. There were native empires that fought each other and fought against the Euro/US invasions to the last, by politics and by war.

I can't wait to see other suggestions or takes on these books. I really want to learn more too!