This is a fairly powerful question and the subject of many books. To offer a comprehensive answer through eNotes is a faint hope, at best. Rather, I hope you can see this answer and the others that might follow as a way to begin the process of a reflective dialogue for you to be able to derive your own answers.
Native Americans took many different approaches in working with American government. They hoped that a sense of balance could be struck between settlers and their communities. At some points, Native Americans hoped that the Supreme Court would assist their claim. The case of Worcester v. Georgia proved that the American government had to honor the agreements it made with Native Americans in regarding their freedom, right to their own lands, and the right to be left alone. Yet, American leaders, Andrew Jackson, for example, did not agree and advocated policies that moved the Native Americans more and more West and into a more relegated sense of space and land. As Western Expansion and the Gold Rush translated into White Settlement of Native American Lands, Native Americans tried to launch offensives against this encroachment. Leaders such as Sitting Bull as well as Chief Joseph tried their best to repel the advancement of settlers. Such attempts failed (One is reminded of Chief Joseph's "I Shall Fight No More.) While there were incidents such as Little Big Horn, these were few and far between. Many Native Americans became resigned to their fate, and lived out their culture at reservations or areas where the sprawl of White Settlement could not reach. Native American culture, in its mere exercise, served as an active statement of resistance towards American notions of progress. Their manner of living out their culture, in an isolated setting, accepting the reality of their conditions, but not sacrificing dignity represents a significant part of the American Dialogue.
The African American method of dealing with the challenges prompted by the cultural majority have been well documented. Leaders throughout American History have emerged that have advocated different approaches to addressing the reality of discrimination and denial of opportunity in America. Some of these leaders are common names in American History textbooks: Frederick Douglass, Booker T. Washington, Ida B. Wells, W.E.B. DuBois, Malcolm X, Dr. Martin Luther King, Jr., Stokely Carmichael, Thurgood Marshall were all leaders who advocated different approaches to working within the society where inequality and obstacles had to be approached within American society. Some advocated a sense of "working within the society" in order to make things better, while others suggested that "working outside the society" is the only way to achieve the freedom and equality that is so coveted.