It varies. Britain in India was a mix of negotiation and heavy handed strong-arming. A good book that covers Britain's activities in India and surrounding territories is actually a book on their espionage and proxy war with Russia, The Great Game by Peter Hopkirk.

I'm not as educated in other European powers and their presence in Asia, but Britain usually tried to avoid overt violence, unless they were in a period of Russo-phobia, in which case even a shadow of an Ushenka would have them invading a country if that country did not immediately expel every known Russian agent and recommit themselves to alliance with Britain. In the latter case of policy, it didn't always go well. There were the disasters of the Afghan wars, the embarrassing invasion of Tibet which had a massacre of surrendered troops due to a misunderstanding (and no Russians at the capitol, woops!), and after the rebellion in India, the constant fear of another rebellion.

The danger of a military expedition going embarrassingly, horribly wrong (such as the Boer War), with British soldiers being routed, constantly put pressure on military and diplomatic assets to end things quickly, which in turn reigned in the tendency for violence (although in some cases it would dial it up to eleven, like with the suppression of the rebellion in India). This is because if a war went badly, support for the current government in London could collapse, something the politicians in London wanted to avoid, if they were the party in power.

China and its relations with Britain and other European powers was another story. An empire in collapse, the British and other Europeans were set to carve her up, using all leverage they could both diplomatic and military to insure to have a place for their markets and resource extraction. The slightest resistance was usually crushed, with the Qing imperial government forced to sign ever more ruinous peace settlements until they finally collapsed in 1912.

To give you a short answer, as far as Britain was concerned, peaceful settlements were good, if they got you what you wanted. But the British were fine with using force, if they could get it done quick and cheap.

In Canada (well, at the time Britain) there was the Royal Proclamation of 1763 which acknowledged that natives owned the land and had to be negotiated with. Canada/Britain never went to war with the natives after that in what is now Canada. They signed treaties including the numbered treaties which covers around half of Canada and created reserves and obligations such as money, supplies, health care, and education for them. In fact, some native groups approached the government for treaties because they wanted health care, money, and other benefits. Of course the natives still got pretty screwed though because their services haven't lived up to standards of other Canadians. Also the government is supposed to have a fiduciary responsibility which is supposed to mean work in their best interest, like a defence lawyer getting the best possible outcome, but they have not.

The government also set up residential schools which were schools ran by churches built purposefully far from the reserves and took kids ages 6-18 from their parents (and jailed parents if they refused), sent the kids 100s of kilometers away for 10 months of the year. At school they could not speak their own language or worship their own gods, and got sexually, physically, and emotionally abused, and died under mysterious circumstances or from trying to run away in freezing temperatures. Imagine those reserves without all the joy and laughter of their children, how depressing. So Canada didn't go to war, but damn, it hasn't been pretty. http://en.wikipedia.org/wiki/Canadian_Indian_residential_school_system