The previous answer seems to address the issue of whythe Western industrial powers took empires more than it addresses the issue of howthey did so.
These powers took empires through their technological, military, and economic superiority. For example, the British were able to force China into unequal treaties after the Opium Wars because the British had so much more military power (which comes in part from their economic and technological strength) than the Chinese did. The US was able to exert control over its sphere of influence in the Caribbean both because of its military and because many of the countries depended economically on the US.
By having such advantages, the Western industrial powers were able to take empires.