You didn't specify a time frame, so I'm going to focus on the 18th Century, mainly the early half.

The basic unit of Cherokee society, whether Overhill or one of the three other major divisions (Lower, Middle, and Valley), is the clan system. There are seven Cherokee clans: the Wild Potato Clan, the Deer Clan, the Bird Clan, the Wolf Clan, the Paint Clan, the Long Hair or Twister Clan, and the Blue or Panther Clan. Clans are matrilineal; children inherit their clan identity from their mother. When it comes time for a person to marry, marriages between people who belong to the same clan or one's father's clan were regarded as incestuous. In theory, marriages to someone from your grandfather's clan was regarded as preferable, but in practice this doesn't seem to have been a major concern.

The next most important structure in Cherokee society at the time is the village. Ideally a village is home to members of all seven clans. Populations of a Cherokee village at this time range from between 300-600, whether living in the core settlement or in peripheral households that, while not part of the main part of the village, are still part of its political structure. In the early part of the 18th Century, all Cherokee villages are political autonomous. They were bound together through marriages, summer ballgames and other festivities, etc. It was unacceptable for one village to make war against another; personal disputes were settled by the clans involved, typically with moderation from the uku.

The uku has been described variously as "high priest" and "civil chief." He was at the top of the village's civil hierarchy, and was served by four main officials: an assistant chief or Right Hand, a Speaker, a keeper of the Council House, and at least one Messenger. These men oversaw ceremonies, helped settle disputes, and generally sought to preserve harmony in their society. At least once a year, they also moderated the village council.

While a village council might be called whenever one was thought necessary, a major council was always called at the end of the year. This council lasts for about a month, coinciding with three major festivals beginning with the harvest festival in September and ending with the New Years festival in October, during which any lingering ill-will arising from the council debates is supposed to be washed away.

The Councilhouse is a large seven-sided or circular building near the center of the village. Inside are seven banks of benches. The uku and his attendants sit near the center. An inner council consisting one Beloved Man (an elder, generally over 55) from each clan is chosen. The remaining Beloved Men sit closest to the center, with younger men behind them, and the women and children in the back. There's some confusion in the historical record over how exactly the Beloved Women and the War Women fit into this arrangement, and whether they're one in the same (it seems that War Women are the counterparts of the younger men who have earned the right to speak in council by acts of valor, and the Beloved Women are War Women who have gained elder-status).

When a matter is brought before the council, the clans debate it internally first, then pass their decision on to their representative on the inner council. The inner council debates it for a time, then returns to their clan to discuss how the other clans feel on the matter and how or if they should adjust their stance to come to an agreement. Unanimity was the goal of the council, and several cycles of debate might occur before the clans came to mutually agreeable decision. Facilitating the effort toward unanimity was the deference younger men were expected to pay toward the Beloved Men, and the fact that should anyone be particularly opposed to a course of action he might withdraw from the proceeds and be permitted to go his own way so long as it didn't interfere with the goals adopted by the council at large.

Complimenting the uku and his civil officials was the war chief and his war officials. They were not generally permitted to speak in the council unless the council was voting to go to war. The war chief was generally a younger man rather than an Beloved Man, elected by the other warriors. Like the uku, the war chief had his own set of officials. These included the war priest, war speaker, and physician. He also had an inner council consisting of one representative from each clan. Beneath them were five ranks of warrior, distinguishing by increasingly more notable acts of valor in war. At the vary bottom of the war hierarchy were the unranked apprentices (boys who didn't fight, but were there to help carry and maintain supplies and learn from the warriors) and warriors that had yet to distinguish themselves.

The war chief might also be dispatched on diplomatic missions, which were similarly structured, but generally involved fewer men. On the average, a village might dispatched around 40 men to war at a time (about 100 being the most they'd be able to send). A diplomatic mission would usually only be 15-20 men.

Around 1730, under pressure from Charleston, the Cherokee began forming a national government. Initially the Lower Cherokee, with their closer position to the colonists, rose to national prominence. However, the Overhill Cherokee had long been more politically influential and through this period that influence only grew. With the rise of Moytoy of Tellico, the Overhill Cherokee overtook the Lower Cherokee as the dominant group (though the Lower Cherokee, allying with the Middle Cherokee, tried in vain to counteract the Overhills' influence by attempting to negotiate separate deals with the colonists). Moytoy was a war chief and his nascent national government was an extension of the diplomatic function of his office. However, when Moytoy died, his son Amouskositte took over and proved to be less effective. The role of national leader passed from the war chiefs to the civil chiefs when Old Hop, the Speaker of Chota, became the First Beloved Man. The national government was reformulated to resemble the village government. A national council was assembled annually in Chota, with the various villages sending their uku and speakers along with a small delegation of other beloved men to debate national policy.