Can someone describe the culture and political organization of the Plains Indians? Also, discuss how and why their relationship with white Americans changed from the 1840s to the 1890s.
The Plains Indians were comprised of many tribes, with many differences between them; but certain general patterns of similarity can be found across them.
Most Plains tribes were largely decentralized, with most decisions made at the level of an individual village of a few dozen people. This is likely due to the geography; the Great Plains were very spread out, and thus travel or communication over the long distances was quite difficult. Different villages were united into clans, with social norms expecting people to marry those of other clans in the same tribe. Of course, it would be possible to go into much greater detail about the complex cultures of all these different groups of people; if you have more specific questions please ask them as separate questions.
Instead I'll move on to the question of how the relationship between Great Plains Indians and European settlers changed over time.
For centuries after the arrival of European colonists, the Great Plains were largely ignored by European settlers, because land was not scarce and they didn't seem to contain any particularly useful natural resources. It wasn't until the mid-1800s when the United States began intentionally expanding territory westward (including the Louisiana Purchase, the annexation of Texas, the Oregon Trail, etc.) that Great Plains Indians had a great deal of contact with European---well, now actually American---settlers. This process accelerated in the late 1800s as oil became an important resource, because suddenly the Great Plains had a resource that people were willing to fight over.
A lot of American ideas and attitudes toward Native American populations ("cowboys and Indians") come from this period, which was generally characterized by conflict between settlers and indigenous populations. Eventually these conflicts smoldered down, but not before the United States had annexed almost all of the territory and left only a small portion in reservations for indigenous people.