Wow, so this is a huge question.
Just to be clear, we are talking about five centuries of history on two continents between hundreds of Native American nations and more than half a dozen European nations/former colonies. There is no one brief answer to this question, but I will try to provide some context for understanding the very basics of diplomacy after contact in North America.
First, and I feel silly saying this but the point needs to be made, Native North American diplomacy existed before contact. Europeans entered a system in motion, with nations making war, negotiating peace, forming massive confederacies, major population centers were dispersing and others were forming, while others were migrating across the countryside. Calumet ceremonies, reciprocal gift giving, warfare against traditional enemies, and all manner of negotiation tied communities and nations together. When Europeans arrived they entered this world, and needed to learn the rules of Native American politics if they wanted to survive.
Second, the traditional narrative of contact presents Europeans as the dominant force in interactions with Native Americans. In truth, for the first few centuries in North America, European colonies persisted in the shadow of powerful neighboring Native American nations, and no European colony/former colony gained any manner of hegemonic control east of the Mississippi until well into the 19th century. New World diplomacy needed to be conducted on Native American terms, and the repercussions of failed diplomatic measures on the frontier of North America could reverberate in warfare around the world, as seen during the Seven Years’ War. Europeans who could not, or would not, engage in Native American politics found themselves at least at a tremendous disadvantage in the game of empires, and at worst such failures threatened the very survival of every colonial outpost.
The Pueblo Revolt rolled back the frontier, and ousted Spain from New Mexico for more than a decade. Plymouth Colony barely survived King Phillip’s War. The on-again-off-again battles of the Powhatan Wars constantly threated the persistence of Virginia, and nearly 10% of South Carolina’s white population was killed in the Yamasee War. The threat of annihilation was very real, and though Europeans often grew tired of the Native American style of politics, they needed to play the game.
Native American diplomacy with early colonies reflected their needs and desires, and they used relationships with various European nations to gain negotiating power, jostle for position among traditional enemies, and provide access to trade goods. Three quick examples to show a Native American perspective on our popular stories of contact period diplomacy...
In the wake of a terrible epidemic and under mounting pressure from inland enemies Massasoit, sachem of the Wampanoag Confederacy, reversed an earlier policy of resisting permanent European settlement and allowed the Plymouth colony to stay in Massachusetts. He saw the new arrivals as a way to access trade, as well as a potential military ally, and approached the Plymouth settlement with terms after the starved colonists survived their first winter.
Powhatan/Wahunsunacawh responded to Spanish encroachment from the south and allied over 30 nations into the Powhatan Confederacy. When the English arrived he ceremonially integrated the Jamestown settlement into the Powhatan Confederacy through John Smith, with the intent of using them as a trading and military partner.
Archaeologist John Worth states the Franciscan friars stationed in communities in La Florida functioned like the modern Peace Corps. Friars were granted voluntary admittance into already established, sedentary, maize-based agricultural populations and served to re-enforce chiefly power among the Timucua, Mocama, and Guale caciques. The caciques dictated the terms of the arrangement, using the Spanish to leverage prestige among neighboring rulers, and the military garrison at St. Augustine, if needed.
Because Native American diplomacy served their own needs, rather than the whims of Europeans, they were often perceived as fickle, untrustworthy, and lacking loyalty when they shifted alliances for their own good. Confederacies like the Creek, Choctaw, and Cherokee formed after contact and played the French, the Spanish, and the English against one another as possible, jockeying for trade access, and limiting the flow of goods to their rivals. Nations like the Osage, refugees fleeing inland following the warfare and displacement of contact, remade themselves in the middle of the continent where they rose as the dominant force controlling trade on the threshold of the Great Plains.
The popular perception of colonial history fails to capture the constant negotiation, and re-negotiation, occurring throughout the Americas after contact. In the South after the destruction wrought by the Yamasee War, colonial leaders learned the hard lesson “that diplomacy rather than force was the key to relations with southern Amerindians” (Gallay).
Edit: Sources...
One Vast Winter Count: The Native American West Before Lewis and Clark
The Indian Slave Trade: The Rise of the English Empire in the American South, 1670-1717
Does Canada count?
English-ruled Canada relied much more heavily on diplomacy and trade negotiation than America in its dealings with the First Nations. There was much less in the way of outright armed conflict - though there was still some of that - and the expansion of European settlers into Canada was, by and large, a much more peaceful process. That isn't to say it was without difficulty, just that, as far as imperialism goes, the Canadian version of it involved a lot less bloodshed than the Spanish conquest of Mexico or the American expansion.
And all of that diplomacy was effectively between the aboriginal nations and the government of England. Canada wasn't its own nation until 1867. All dealings with the First Nations before that point would have been effectively dealings with England.
Moreover, alliances were sometimes made between English/Canadian military forces and those of the First Nations. During the War of 1812, for instance, thousands of First Nations and Metis fighters were involved defending Canada. Dakota, Ojibwe, Odawa, Pottawatomi, Shawnee, Algonquin, Mohawk, Huron and Abenaki were all integral to the fighting, both defensively and offensively (the Ojibwe, Odawa, Pottawatomi and Shawnee were all part of the capture of Detroit).
Maybe most importantly, the division between Canada and the United States was entirely artificial from a First Nations point of view. The 48th Parallel goes right through a lot of native territories, and those territories were generally more important than the distinctions drawn by European settlers. Algonquin territory is enormous and covers huge swaths of Canada and the United States. Much of Canada's dealings with the First Nations peoples involved dealing with Native Americans, as the groups involved didn't make much of a distinction between American Ojibwe and Canadian Ojibwe.
Source: You can find a lot of really great information about Canada's history (and current affairs) involving the First Nations on the Aboriginal Affairs website, including information the Metis revolutions in Manitoba and Saskatchewan and on the relationship Canada has had with the First Nations since Confederation.
When? Which time period?