Can you specify? Is there a particular band you'd like to know about?

Very broadly speaking, Cherokee sided with British due to frustration over American incursions into their territory. Many New England Native Americans sided with the Americans and joined militias. The Six Nations of the Iroquois were split, with the Oneidas and Tuscarora siding with the Americans and the Mohawk, Onondaga, Cayugas, and Senecas siding with the British. Native Americans of the Ohio Valley tried to remain neutral, but following American massacres in the region, joined the British and resisted American incursions into the Ohio Valley.

American militias defeated the Cherokee in the south. While an American force known as the Sullivan Expedition, devastated the Iroquois and drove them out of their homeland in 1779. Overall, the Revolution was like a civil war for the Iroquois.

In general, following the war, Native Americans were cleared from most lands east of the Mississippi. Although some groups had supported the Americans, most Americans viewed the Native Americans as supporters of the British and had few qualms at taking their lands.

For a good brief rundown, see https://www.nps.gov/revwar/about_the_revolution/american_indians.html

Also, see the sources on that page for further reading, specifically works by Colin G. Calloway, Woody Holton, Richard White, R. Douglas Hurt and Francis Jennings.

So broadly speaking, many of the native tribes had their own reactions to the war, which meant they picked their sides depending on how they could benefit. It is too generalizing to say they all went for one side or the other, as some sided with the Americans just as others sided with the British. The Oneidas from the Iroquois and the Catawba in South Carolina sided with the Americans, while others like the Creek and Cherokee sided with the British. Many actually tried to remain neutral, especially at first.

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I did my MA on the Cherokee in the American Revolution so I can probably give you more of an answer on that. The Cherokee at first tried to remain neutral, even though they had complained to the British government about Americans settling on their lands, not to mention many land deals such as the Henderson Purchase which ended up trading nearly all of modern-day Kentucky to land speculators. However, the Cherokee neutrality did not last too long as the more warlike segment of the Cherokee, led by Dragging Canoe and his young warriors, decided to make war on the settlers in Virginia, the Carolinas, and Georgia. Dragging Canoe's party, later dubbed the Chickamauga Cherokee from the creek they settled by, saw the war as a way to regain their lands. They feared that they would eventually be surrounded by Americans and cut off from their traditional hunting grounds. Land was the main source of contention for the Cherokee, as well as other tribes. Land was their connection to their tribal traditions: hunting, war, tribal communications, burial grounds. The Chickamaugas saw the war as a way to prove themselves as Cherokee warriors.

The British wanted to use the Cherokee and other southern tribes as an auxiliary force in the backcountry in order to take a foothold in the south while the Army would invade the coast via Charleston and Savannah. The British plan ultimately failed after some disastrous attempts to take Charleston, and many of the southern natives lost of a lot of the support they wanted in the frontier. The Americans retaliated against the Cherokee with expeditions, destroying many of their towns, and eventually the Cherokee peace party, led by Little Carpenter, capitulated to the Americans.

Now, the thing is at this point, the Cherokee were kind of split at this point with the peace party and the war party. Little Carpenter and the his elders spoke for peace to the Americans, who thought they spoke on the behalf of all Cherokee, but Dragging Canoe continued to attack the Americans for the next several years even after the Cherokee made peace with Virginia and the Carolinas in 1777. The peace party hoped that appeasing the Americans would mean less destruction of their lands and save the lives of their people. They maintained that they were friends with the Americans, and the blame was with Dragging Canoe's party. During the peace treaties, it became evident to the Cherokee peace party that they were not going to get the lands they lost in western NC back, but they could at the very least prevent any more being lost and hoped for a strong barrier between the Americans and the Cherokee.

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Ultimately, the Cherokee did end up losing much of their lands and were pushed towards the south and west after the end of the war. For them, the fight against encroachment was also their way of retaining sovereignty and independence, and I'll claim that it was the early start of Cherokee nationalism that really grew by the early 19th century.

I had a long list of primary sources I used for my MA, from the NC Colonial and State Records, the Calendar of Virginia State Papers, and the Draper Collection. Some secondary sources that pull from this are Colin Calloway's The American Revolution in Indian Country, James O'Donnell's Southern Indians in the American Revolution, Richard Blackmon The Dark and Bloody Ground