Even considering the 'beach-head' of missionaries and merchants most powers would have had, this doesn't explain how they could assert control over a foreign land to me. Especially, how did they build the tools of administration necessary to practically assert control?
And if they simply relied on pre-existing native administrations initially, how and when did they make the transfer to a colonial administration, if at all?
You're going to have to be more specific in your question. There was no one, tried and true, method of asserting control over the entire imperial system, from Africa to Asia, among the various imperial powers, whether the big ones like France and the UK or the smaller ones like Germany or Portugal. Some colonies were settler colonies, others were not. Some were controlled by corporations, others were controlled directly by the governments of the imperial nation, still others were the personal property of the monarch, and these statuses changed over time, depending on any number of factors, including local politics in the motherland or events on the ground in the colonies themselves. There are simply too many variables to give a blanket answer that could work for any group, let alone all, of the various colonies.