Alright, my turn to shine here!

So, the Native American conflicts are a big topic, and the answers to your question are as varied as the tribes that once lived there. I’m assuming that you are referring to the period of time between 1850 and 1900, which Americans generally refer to as the Indian Wars. I’ll use a couple different examples, both of which are pulled from Bury My Heart at Wounded Knee, as well as similar historical and anthropological works.

I’ll begin in the Southwest with one of the classic examples of Native Americans resisting US rule, the Apache tribes. Here, we have a group of people that resisted the Spanish, the Mexican, and even the US efforts to subjugate them. These people fought long and hard, and had won several victories against the Westerners, and there was a period that they had negotiated peace with the various governments, allowing them to continue living in their mountain strongholds. However, this was not to last, as the US government moved to expulse the Natives from the land in order to made room for farming, mining, or ranching. At this point, the Apache did fight, and fight hard. The US did not ultimately subjugate the tribes until they found and destroyed the oases within the mountains that the Apaches used to grow their crops and keep their horses. By this time, however, the remaining fighters had all but lost anyways, and ended up folding under this final blow.

If we move northwards, towards the Great Plains, it gets more complicated. There, you have the Sioux, Cheyenne, Shoshone, Crow, and other “classic” tribes in the historic sense. These tribes are where we get the image of the typical Native American people, hunting bison, herding horses, and living in nomadic tribes. Many of these tribes actually sought out to live in harmony with the US, and sought to strike deals with the government. Unfortunately, conflicts began to break out as settlers began to take more and more land, and young Native American warriors began striking back, stealing cattle and household goods. This constant friction was commonplace in any border settlements, and frequently ignited local conflicts. The problem was, these conflicts compounded and bred animosity between the white settlers and the Native tribes, and eventually became so great that the US sought to solidify its control over the border by stationing troops and using force against the Native tribes.

After this, we begin to see the outbreak of the larger campaigns against the Native Americans that the US calls the Indian Wars. According to Native historians, the Native Americans did not think to conquer the US, or even to take back territory from the white settlers. Rather, the Native tribes that did strike back did so because they did not feel that the US was living up to its end of the bargain, settlers were moving into lands claimed by Native Americans, and roads and railroads were being constructed across Native lands. They felt that the US had betrayed their trust, and if they responded, perhaps they could convince the US government to keep its citizens in line. So, from the Native tribes’ perspective, they were defending the lands given them by various treaties signed by the US government and the tribal leaders.

These conflicts escalated quickly. Once the US Civil War ended, the government had a surplus of veteran troops and material that could be sent to the frontier in order to combat the Native tribes. One of the most iconic conflicts to come out of this period was the Great Sioux War in 1876, over the ownership of the Black Hills. As had happened before, the white settlers living near Native territory began encroaching on Native American lands, and Native Americans began to strike back. The US government became involved, and large-scale conflict broke out. This conflict spawned one of the classic battles in American myths of the West, the Battle for Little Bighorn. Once again, the Native Americans believed that they were defending the lands and rights afforded them by treaties previously signed.

Speaking just about the Northern California wars of 1850-1870 the vast majority of adverse encounters were not "army against army", in the sense of nation against nation. Rather, they were battles against a village or individual by another individual, militia or Army unit. In this protracted period of hostilities, that include the Indian Island Massacre, the Bald Hills War, numerous battles on Eel River, Redwood Creek and Trinity/Klamath, and later, the Modoc War, natives were generally just trying to survive. They had little understanding of the "United States" other than their familiarity with its Army. At least initially, there was no intention by the natives to "go to war" with the whites. It would have likely been impossible to build a coalition among the disparate tribes to actually mount an offensive against the Army or the whites in general. Alternatively, many white individuals and communities called for all out war. County governments were dead set on displacing the natives by any means at hand. Many thought that extermination was inevitable. The Chico Courant (newspaper) on the "Indian Problem":

Nothing but extermination will keep them from committing their depredations. It is a false notion of humanity to save the lives of these Red Devils. There should be no prisoners taken, but a general sacrifice made of the whole race" (Lindsay 2012:211

Or the state position:

That a war of extermination will continue to be waged between the races, until the Indian race becomes extinct, must be expected. While we cannot anticipate this result but with painful regret, the inevitable destiny of the race is beyond the power or wisdom of man to avert. - Governor Peter H. Burnett, January 7, 1851

The vast majority of skirmishes in Northern California were caused by volunteer militias hunting Indians down using any possible rationale. If some cattle were missing, militias would be called to find some Indians and kill them and burn their houses. It should be noted that militias and individuals made little distinction between guilty Indians and any Indians. The most common pattern in Northern California was that the Indians who were attacked in retribution for depredation had nothing to do with the original event. An entire village in Trinity County was destroyed because "two miners were missing in the mountains". Miners were always missing in the mountains. That is what gold prospecting is. Another white strategy was to capture Indians and send the men to a far away reservation and "adopt" the women and children. This was, in fact, a kind of legal slavery (Lindsay 2012:191). Natives reacted in kind by perpetrating small raids on miners and settlers.

Lindsay makes a compelling case that the militias were consistently reimbursed by the State of California for their time and expenses. This turned into an employment program for cash-strapped settlers and many who found mining too difficult or simply ran out of money. Many conflicts occurred because it was in the members of the militia's financial interest.

Since the Indians had been displaced, murdered and harassed for decades, their traditional subsistance practices were completely disrupted. This caused them, at times, to prey upon domestic livestock. Northern California natives still jokingly refer to cattle as "slow elk". However, the response by County Governments, militias, and individuals was completely out of proportion to the settlers' losses and included murdering the residents of and burning entire villages or groups of villages.

I do not think it is safe to say that the natives in Northern California ever expected to win. I believe that they were just trying to live to see tomorrow. With regard to the Modocs, Captain Jack initially thought he could broker peace with the Army and get a reservation on Lost River. The Modoc had been forced onto a reservation with their traditional enemies the Klamaths. That was the root cause of that war. Once fully engaged, it appears that the Modocs were just trying to survive. You should note that the Modoc primary tactic was one of strategic retreat.

Source: Murder State; California's Native American Genocide, 1846-1873. Brendan C. Lindsay, University of Nebraska Press. 2012