The British Empire, at it's zenith, covered almost 1/4 of the world's land, and almost 1/4 of the world's population. First of all, to answer this question, you must know what colonialism is. A dictionary definition of Colonialism is to "the policy or practice of acquiring full or partial political power over another country, by occupying it with settlers, and exploiting it economically." Now this means that the "mother country" (in this case England) would send over their own people to live in another country. They would pretty much tell the indigenous people that their traditional ways are barbaric, and that indigenous people must do things the "civilized way", and enforce it. As you know, the British Empire had quite a powerful military. They were able to enforce their ways on indigenous people quite easily. Most regions that the British colonized were very much under British control. Take British India for example. The native peoples were slaves to many of the British. Any uprisings would be "put down" through the use of violence. If you go on YouTube, you might find a video (i forgot the name). Its about the British colonizing India; It goes somewhat along the lines of:
British Soldier: We're in charge now, you must obey our rules
Indian Man: What? You can't just come and take our land! We've lived here for centuries!
British Soldier: Do you have a flag?
Indian Man: No... But our ancestors-
British Soldier: No flag, No Country. That's a rule that I've just made up and I'm backing it up with this gun.
Although this is not an accurate description of what happened, the creator of this movie certainly got the gist of what happened. There is a lot more that we can talk about, such as positive or negative impacts of colonialism, but that would be another question. I suggest you go on Answers.com and search "colonialism". I'm sure you'll find a load (tip: look in the Wikipedia section)