The question focuses on the various Native American pre-Columbian civilizations in the New World, and what occurred to them once Europeans began to arrive in the late 15th century. Because the questions relates to post-contact events, we will only look at those groups located in the areas most directly explored by Europeans in the 15th and 16th century. In North America, these were tribes associated primarily with the Mississippian culture. In Central America, the most well-known cultures were the Maya and the Aztec, and in South America the Inca are most familiar. However, note that there were in fact dozens of other cultural groups and traditions living in these areas as well. The reference below would be instructive for more detail.
Overall, this is a massive topic, so simplification and narrowing is needed. As such, we will not address other groups with whom contact occurred significantly later, such as the Plains and Western US based tribes, nor will we look at longer term events, such as the interaction of the native tribes with European immigrants in the US from the 1600’s on.
Let’s start with some basic principles for what happens when people of different cultures interact. These effects can be classified in terms of culture, political power structures, and access to /control of resources. Each group will initially view interaction as either a threat to all of the above, or as an opportunity to enhance one or more of these areas. Also note that we then to talk in generalizations, describing cultures and nations as a whole, as if they were individuals, but in fact each culture is made up of individuals who may possess a variety of attitudes regarding the above areas. How events play out can be materially affected by the actions of specific individuals, so generalizations need to be viewed with some caution as to the degree to which they are determinative of events.
That being said, the peoples of the Americas in the mid-15th century just before contact with the Europeans displayed a wide mix of well-developed cultural, political and economic structures. The North American cultures tended toward less permanent settlements, while the Inca, Maya and Aztec (and the many smaller civilizations of the region) developed complex, well-settled cities with substantial monumental architecture and complex political structures supported by formal taxation arrangements. The more southern cultures also had deep religious traditions with formal clergy. In other words, they were similar in many respects to the monarchic/religious structures reflected in the European cultures with which they came into contact around the turn of the 16th century.
There were two key differences between the Europeans and the indigenous peoples that will be focused on in this discussion. First, and most prominent, was that the European explorers possessed far superior military technology, most importantly the firearm and cannon. This allowed them to create the appearance of military power far out of proportion to the relative numbers of personnel involved. As military victory often results from convincing an opponent that they cannot prevail, rather from actually harming or controlling their forces, this allowed the Europeans (especially the Spanish in the Central and South American areas) to dominate cultures with relatively small numbers of troops and ships.
The second factor was European attitudes formed by the intellectual roots of the Renaissance. This created an expansionist concept of Europe’s role in the world. It was also coupled with a belief in man’s dominion over all of creation, to some extent outweighing the previous sense of humble subservience to the whims of God and Nature. This provided a philosophical foundation for the belief that European control of other peoples was in some sense “rightful”.
A related, and important, difference was the concept of property rights, especially as regards the more northern indigenous peoples. These tribes tended to view such rights as communal within the tribe. That is, tribes negotiated or warred over rights as a whole, but within a tribe property and resources were generally allocated according to communal principles and processes. There is substantial literature analyzing the extent to which this led to fundamental misunderstandings about what was being traded and agreed to between these peoples and the newcomers.
The net effect of these interactions varied among the various indigenous peoples. The Central and South American cultures were generally subjected to outright conquest. Ultimately, their high level political structures were destroyed and their cultures were held in control, primarily for the purpose of providing labor in the service of providing raw materials (especially gold) and agricultural products to their Spanish rulers. Indigenous religion was rooted out and forcibly replaced with Catholic Christianity. The Spanish also controlled areas in the far southeastern portions of the US, but the indigenous peoples there had no significant natural resources worth taking, and their more mobile social structure meant that, in general, they were driven out of native areas rather than being subjugated within them.
In the North American areas beyond modern Florida, there was minimal interaction with Europeans through the 1500’s. When settlement began in earnest in the early 1600’s, the primarily English immigrants initially attempted to interact with native peoples on the basis of the general principles of 1600’s England. In the short term, conflict with native peoples was not widespread. Eventually, the large numbers of immigrants, and the quest to bring more and more land into their system of political economy, became incompatible with indigenous concepts of communal ownership and “usage” of vast areas of land without the structures of actual control. Beyond the scope of this question, this led to direct conflict, in which the military (and by then numerical) superiority of the European peoples ultimately held sway. The net eventual result was the complete marginalization of the native cultures.