This is, of course, an extremely general question, making answering it difficult. I'm sure it looked different for each colony, each empire, and each time period. But I am wondering if there are ANY generalizations that might be insightful.
To narrow the question, I am especially interested in the European empires of 19th and 20th centuries. For example, a part of Africa "becomes" the colony of German East Africa, and then WWI happens, and then this land "becomes" British and Belgian territories. Or, the land that is now Poland changing hands between empires.
What did this mean for the native people of these kinds of places? Were resources simply carried off and expended as empire saw fit? Or was trade more equitable? To what extent were existing native social systems kept intact? To what extent was a military presence or violence used to keep the imperial system going? Were there examples of colonization that Empires saw as "successful" and tried to replicate? How did the native people view themselves and these Empires?
I study Micronesia, which is notable (among other things) for having had many successive colonial occupations -- Spain, Germany, Japan, and then the United States. Some of what happened during the transitions was fairly universal. All colonizers, it seems, love a good flag raising ceremony. This ceremony in Yap is fairly typical, in that in incorporates both the former colonizer (Spain) and the new colonizer (Germany). Due to a bizarre back-and-forth between Spain and Germany, there were actually more flag-raising ceremonies here than there were colonial regimes -- as both nations repeatedly claimed the region until the Pope settled the dispute. But that's neither here nor there.
All of the handovers of power here were broadly similar. A warship touring through the major islands, a flag-raising ceremony, a handover of documents and facilities, sometimes a bit of friendly advice from one governor to another. The Spanish governor of Pohnpei, for example, informed the incoming German governor that without more soldiers he'd be "dead within a week." Then the former occupier would depart and never return.
In order to avoid confusion, each of the colonial powers here has, upon taking power, immediately ordered that all existing laws are still in effect. That happened in the transition to independence as well -- and the case law of the Federated States of Micronesia still takes American-made legal decisions as precedent. For the most part, there hasn't been much in the way of extractive colonialism here. At places like Angaur, which had substantial phosphate deposits, mining activities were simply continued under the new regime. So there really weren't any resources to carry off.
The other questions are too dependent on local context to answer adequately, and Micronesian examples wouldn't be much help. Yes, there were various philosophies of colonial governance that colonial administrators everywhere leaned towards -- but that would depend on the regime and the administrator. Otherwise, I hope it's enough to say that colonialism is extremely diverse and very difficult to describe with a single definition. And, as one might expect, indigenous responses to those regimes are no less varied. I hope that helps.
Not sure if you are looking to do more in depth research on it but Timothy Parson's book "The Rule of Empires" is all about how empires operated throughout different periods. His general argument was that empires operate fine while they are able to distinguish subjects from citizens in order to extract wealth/resources/etc from subject populations, once this barrier breaks down the empire begins to fall apart.