Here are a few of my older posts that you might find interesting. Feel free to ask any follow-up questions you might have here.

• How sophisticated was the Iroquois Confederation's government at its peak? While I'm mainly focused on the men's Grand Council at Onondaga in that most, I should have also mentioned the women's Clan Mother Council at Gaustauyea. We know a lot less about the Clan Mother Council than we do the Grand Council.. In this post I discuss the fates of both councils following the Revolutionary War.
• How was Overhill Cherokee government and society organized? This post is concerned with the political system of the Cherokee in the early colonial period.
• In What native tribes lived in Spanish-claimed Florida, before the Seminole arrived? How were the politics and trade between these tribes?, I discuss 3 cultures from Contact era Florida: the Calusa, the Timucua, and the Apalachee, including the basics of their government.
• In this post I talk about ways in which crimes were handled by various nations. Be sure to check the linked post there that goes into greater details regarding crimes in Wendake, the homeland of the Wendat (Hurons).

Also, I could have sworn I had post somewhere discussing the political system of a few other nations, like the Powhatans and the Natchez. Since I can't find those right now, here's a very quick run down:

• In the Powhatan system, the mamanatowick was the primary leader. This position was passed on through matrilineal succession upon the mamanatowick's death. So Wahunsenacawh ("Chief Powhatan" to the English) passed his title onto his brothers, not his children. Women could also become the mamanatowick, as we see when Cockacoeske, who was the last leader of an independent Tsenacommacah (as the Powhatan's referred to their territory). Beneath the mamanatowick, there were two ranks of weroances. These were essentially the "governors" and "mayors" of Tsennacommacah, overseeing either regional or local affairs. In both cases, the position was hereditary, as long as you kept your superior happy. Otherwise, the weroance could be replaced. Women could also be attain this rank, in which case they were called weroansquas. At all levels, these officials had a council of advisors composed of members of the priesthood and by cronnocos - elevated commoners. While even the mamanatowick might engage in common labor on occasion, generally the mamanatowick and the weroances were supported by a flow of tribute up through the hierarchy.

• In the Natchez system there are three main classes of individuals. At the top are the Great Sun and the Female (or Mother) Sun. The Great Sun is leader of the primary leader of the nation, though colonial (and many modern) texts typically exaggerate his authority and portray him as having despotic control over his people. In truth, the Great Sun had to work with a council of Suns (Suns being the general nobility of the nation). Additionally, the Great Sun and his council was subject to at least partial veto power by the Female Sun. As the mother of the heir, her job was primarily focused on keeping the current rulers of the Natchez from screwing things up for the next generation. The Great Sun's right hand man was the Tattooed (sometimes translated as "Stung" ) Serpent* - though this might be the name of the name of the man who held that position during French colonization rather than his title. In any case, the Tattooed Serpent's job primarily to serve as the military commander for the Natchez. The rest of the Suns formed the nobility of the Natchez, with many serving as priests, village leaders, military leaders, or some combination thereof. Beneath them were the Stinkards, the commoners. Under Natchez rules regarding marriage, Suns could only marry Stinkards suggesting that this historic class division began as a moietic kinship system (which divides society in two moieties). Your class was hereditary though, based on whatever your mother was. So the Female Sun's children were also Suns. The Great Sun's children were Stinkards.

*As a side note, the funerary traditions of the Natchez Suns is particularly infamous since it involved human sacrifice. When the historic Tattooed Serpent died, the Great Sun had to be restrained by his advisers to prevent him from joining the Tattooed Serpent's sacrificial entourage. Apparently the two had made a pledged that they'd enter the afterlife together.

Glad you asked this question! There are a lot of parts to the answer, so bear with me.

First and foremost, not all Native Americans were Hunter - Gatherers (HGs). Today there are over 500 federally recognized tribes, but the number before contact was certainly larger. Most Americans have the impression of Plains tribes like the Yankton (Western Sioux) which relied upon hunting and gathering. However, groups such as the Hopewell relied upon farming in addition to foraging/gathering.

The social organization differed dramatically amongst groups. In Anthropology, “political organizations” are divided into bands, tribes, chiefdoms and states. Bands are the smallest groups with a maximum of about 50 people (some anthropologists will say 100), and they are typically kin-based. Society at this point is typically egalitarian (not to be confused with equal) with work being equally valued. Leaders are most likely charismatic and their influence is due to their achievements. When there is tension in a group, fissioning will occur. Authority is earned rather than inherited.

Tribes are larger than bands, with several kin groups, with greater population densities. These individuals may exist in various autonomous communities. Status is still most like earned at this point, with decisions made by headmen. Social stigma will typically keep people in line - without the group, chances of survival are little.

In Chiefdoms, population increases along with a complex hierarchy. There is a chief as a central authority, and class division first occurs. Mortuary evidence will show in these societies grave goods with children. As they did not have a chance to earn their status themselves, it’s been inherited at this point. Kinship is still an organizing principle, and distribution of goods or luxury materials is held in the hands of the elite classes. Punishment can also be imposed on those who violate the rules (such as disloyal bands). This is most likely organized through same-clan support.

In state level societies, there is a formal political organization with rules and a centralized government. There is less reliance on kinship at this point, and more wealth, sedentism, inequality and ranking. There’s some debate in American archaeology as to whether the site of Cahokia is a chiefdom or a state. However, the Aztec most definitely are.

I recommend checking out some intro archaeology books such as Wendy Ashmore’s “Discovering Our Past: A Brief Introduction to Archaeology,” or “The Past in Perspective by Kenneth Feder.” If you’re interested in HGs specifically, ethnographies are a good place to start. The !Kung are a tribe that have been studied extensively by anthropologists.