Warrior societies were common among Plains tribes, some with surprisingly strict hierarchies. A great deal of knowledge about these have been lost or purposely suppressed in the late 19th and early 20th centuries. The Kiowa's still have their Black Leggings warrior society, that's active today. Cheyenne still have Dog Soldiers today. Many of these men serve in the US military now.

For a glimpse into how complex ranks in Native American militaries once were, Arapaho men used to have "lodges" or societies that were organized by age group. Youths belonged to the Kit Fox lodge, then the Stars, then Club Board (Tomahawk), Spear, Crazy Lodge, Dog Men, Old Men, and Seven Old Men lodges. According to Jeffrey Anderson (who is it if you want to know about Arapaho society), the Spear Men served as military police in the camp, the Club Board Men were the first to charge into battle, the Dog Men led the younger/lower ranks. In battle, Dog Men would push a staff into the ground and fight for that ground until victorious or released by another warrior (Anderson 24).

To serve as a chief, who would coordinate attacks, a man had to at least achieve the rank of Dog Man (24). The Seven Old Men were the most respected elder men in the tribe who conducted ceremonies.

Activities in battle were complemented by ceremonial and dance activities. Each of these ranks had highly specific regalia (sashes, etc.).

Going back to the earliest period of European contact with the Haudenosaunee, matters of war and justice (intertwining concepts) were private affairs, organized on a local - usually family - level. The most common variety of military campaigns at this time were the mourning wars. When a member of a family died suddenly, perhaps by disease or from an attack by an outside group (the Great Peace provided other means of resolving internal conflict), the women of the family might call for a mourning war to avenge the family. Preferably the culprit of the crime would be the target, but if they were unavailable any long-standing enemy would suffice. An appropriately charismatic and experienced man within the family would make the formal call to arms, rallying other men to the cause. For men, participation in such conflicts was important because military experience was a vital component to social mobility.

Typically mourning wars were relatively small and bloodless affairs. Ideally captives would be taken back, to be judged by the family's women and either adopted or executed as suited their sense of justice. Execution, while infamously torturous, was rare, normally chosen only when the offense that sparked the mourning war was still fresh. Killing the enemy in combat could also satisfy the demand for justice but was less than ideal; the offended community neither receives a person to compensate for their prior loss nor public execution for a communal catharsis.

Mourning wars could grow into quite large conflicts, if additional families, communities, or nations felt the same call to arms. Still, these were grassroots campaigns, building momentum up from the bottom rather than being commanded from the Grand Council. Each family or community that rallied men to fight had their own commander, and these would convene among themselves to organize their men. They would travel together toward their target, but once they were close each commander would take his own men and fan out, each carrying out their part in the overall strategy or striking out as opportunities arose.

The Grand Council had little say in these sorts of wars. If the Seneca decided to declare war on the Miami, their representatives on the council would bring the issue up and offer the other nations a chance to join in. Even if the other four (or five, post-Tuscarora) voted not to go to war, the Seneca could still carry out their campaign on their own, barring some peculiar situations where that campaign might directly conflict with the goals of another member of the confederacy.

By mid-1600s, the focus of Haudenosaunee military campaigns shifted, increasingly becoming a confederacy-level concern. On this level, the Haudenosaunee constitution appoints five war chiefs, one from each of the original Five nations. They're primary purposes was to policy the roia:ner / hoyaneh (the representatives on the Grand Council), to make sure they performed their duties and punish those who abused their authority. The roia:ner were barred from joining in any military campaigns while they were in office, but could take an official leave of absence to participate. The Haudenonsaunee constitution also provides two causes for unified war. One is during an invasion, at which time it fell to the five war chiefs (or to their appointed messengers) to get back to their respective nations, raise the alarm and mount a defense.

The other cause is ideologically driven. The Haudensaunee viewed mourning wars as a necessary evil, but an evil nonetheless. The Great Peace abolished mourning wars between the members of the confederacy, and in a perfect world, all nations would be brought under the auspices of the Great Peace. Repeated refusal the accept the Great Peace was grounds for war, and this was employed during the Beaver Wars to justify Haudenosaunee expansion (it wasn't the only method of justification though - the war against the Miami began as a border dispute and, of course, there were economic benefits to be gained by these campaigns as well).

The Grand Council would vote to extend membership to another nation (of course, if a nation accepted they became non-voting members of the confederacy), and once that nation refused three times, one of the roia:ner had the responsibility to inform the five war chiefs. From there, the war chiefs again would rally men throughout the confederacy to fight. Those who joined the war elected one of the five war chiefs to serve as the general for that campaign.

This often mention the complete dismantling of the enemy nation, as happened with the Wendat (Huron) and other neighboring Iroquoians in the earliest campaigns of the Beaver Wars. Those who were dispersed among the Five Nations as adoptees would eventually create a new confederacy, the Wyandot, outside Haudenosaunee influence. Others accepted the Great Peace without putting up much resistance, such as the Lenape (Delaware) and the portion of the Shawnee that fled east after losing a war to the Chickasaw-Cherokee alliance early in the 1700s, both of which would largely regain their independence by the time of the French-and-Indian War. The Beaver Wars aren't likely to be the first time the Haudenosaunee engaged in such large scale efforts; most of the Dhegihan-speaking people (the Osage, Quapaw, etc.) recall an earlier Iroquoian expansion that pushed them out of the Ohio (whether this was the Haudenosaunee, a proto-Haudenosaunee alliance, or some other Iroquoian group is debatable).

I mentioned earlier that a member nation could conduct their own military campaigns barring some peculiar situations where that campaign conflicted with the goals of another nation within the confederacy. Such a situation came up during the American Revolution, with the confederacy divided over who, if anyone, they should support in the war. The dispute caused deep, and occasionally bloody, divisions in the confederacy that led the Grand Council fire being extinguished and the confederacy being dissolved (it would, however, reform as the Six Nations of the Grand River in modern Ontario after the revolution).

Sources:

Morgan, Lewis Henry. League of the Ho-dé-no-sau-nee Or Iroquois

Keener, Craig S. An ethnographic perspective on Iroquois warfare during the second half of the Seventeenth Century. The Ohio State University. 1998.

Richter, Daniel K. War and Culture: the Iroquois Experience. The William and Mary Quarterly. v40.n4. 1983.

Snow, Dean. The Iroquois

The Gayanashagowa