Are you looking for day to day life of the Native American tribes or the way the tribes of the confederacy interacted with one another from an intergovernmental standpoint?
I can't speak for every tribe in the confederacy, though there are many similarities among Iroquoian, and even Eastern Woodland, tribes. I can, however, give you some information about my tribe, the Oneidas.
The Clan System
The clan system in any of the tribes is the basis of social and political structure. The Iroquois have a total of nine clans, three of which are incorporated by my tribe, the Oneidas - the Bear Clan, Turtle Clan, and Wolf Clan. Each is considered a matrilineal unit with certain responsibilities.
Wolf Clan - known as the pathfinders. Their responsibility is to guide the people in living their lives in the way the Creator intended. During government meetings and ceremonies the Wolf clan is responsible for opening the meeting and setting the agenda.
Bear Clan - keepers of the medicine, or healers. Bear clan people retain knowledge of all medicinal plants on earth.
Turtle Clan - in the Iroquois creation story, the earth was created on the back of a turtle. The Turtle clan (my clan) are considered the keepers of the land and our responsibility is everything to do with the environment.
The Great Law tells how all members of each clan have a relationship to each other. Laws of clanship are rigid - in the past it was forbidden to marry a person of the same clan, even within the Iroquoian tribes (i.e. even if one person were Mohawk and the other Oneida). The Wolf Clan is considered a cousin to the Turtle Clan and an uncle to the Bear Clan. The Turtle Clan is the older brother to the Bear Clan. This familial/relational understand becomes important during ceremonies and for making political decisions.
There are chiefs, clan mothers, and Faithkeepers (below) from each clan. For Oneidas there are 3 clan mothers and 3 chiefs for each clan, and 2 faithkeepers for every chief (one male and one female).
Familial Structure & Gender Roles
As I said, Iroquoian people are matrilineal, which means your clan identity is determined by your mother. When a man marries he moves in with his wife's family. The woman's family would then include her mother, father, brothers, sisters, aunts, uncles, cousins, grandmothers, and grandfathers. The women of the household took care of the children. Any and all children of the household were considered a son or daughter. Aunties were looked to as mothers (still are in my family). Uncles were looked at as father figures and grandparents/elders were most respected (still are).
As children grew the older boys would go with the men to learn how to hunt, fish, and gather wood. They also learned how to fight as well as their roles in ceremonies. Some were chosen at a young age for leadership roles in their clans. Older girls and all of the younger children would stay home with the women who were also the primary caretakers of the fields. They took charge of planting, weeding, maintenance, and harvesting of crops. Men only helped when extra labor was needed.
History and moral teachings were passed down through oral stories. Elders would tell these stories to children to teach life lessons that they could apply to every day life.
As young boys became men they would travel to court women. He would tell his mother who she was and who her family was. Then his family would prepare a basket of food for her family and her parents would determine if he were suitable for their daughter to marry.
Clan Mothers
Clan mothers are responsible for appointing the chiefs on behalf of the people. Clan mothers watch boys from when they are very young and select them for special training if they think they show the maturity for leadership. Clan mothers have the first and last say in guiding the chiefs to help the people. Think of them as the "state" representatives. They are responsible for listening to the family units and are counselors of the people. If you had a problem you could go to the clan mothers for advice and they could elevate that problem to the chiefs if need be.
I should note that this system broke down when Europeans arrived to the "new world" as male warriors in the tribe gained influence and power the more tribes clashed with the settlers.
Chiefs
In addition to leading the people with the guidance of the clan mothers, chiefs also conducted ceremonies in cooperation with the faithkeepers. Once chiefs are chosen by the clan mothers he serves until he is no longer able to serve or passes away. Chiefs also represent the nation to the Grand Council of the Six Nations.
Faithkeepers
Faithkeepers carry out the actions that the clan mothers, chiefs, and community decides. They are responsible for the wellbeing of the people and act as spiritual advisors. They keep track of the calendar and let the community know when it is time for an event or ceremony. They get the longhouse ready and/or the grounds for these events and make sure that ceremonies are conducted as they should be. Their primary responsibility is to ensure that the four sacred ceremonies are held - the Great Feather Dance, Men's Chant, Drum Dance, and Peachstone Game.
There's more if you want to get into the longhouse structure of families or broaden out and talk about these systems for each tribe in the Confederacy (I know less about that). But this will give you a good start to understanding some social structure.
Of course, things have changed greatly with the arrival of Europeans, the breakup of the Confederacy after the Revolutionary War, and even my own tribe that branched off into the Oneidas in Canada and the Oneidas in Wisconsin. And, of course, all of the assimilation policies mean that the structure of the tribe remains similar today, as do some ceremonies, but a lot of what I described above is a bit different as knowledge left us through boarding schools or prior to the Indian Religious Freedom Act of 1978 when it was illegal to practice our ceremonies.
I'm currently studying my tribe's history and teachings to start a podcast, so I'm not a historian by profession. This all comes from my personal experience and studies.