How did the Western industrial powers gain global empires?
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.
The western powers were strongly influenced by the successes and advancements of the Industrial Revolution, especially regarding advancements in transportation, communication, science and technology. These developments emboldened the western powers and made them believe they could practically control the whole world, especially where economic and military strength were concerned.
The western powers were also influenced by the "humanitarian / religious" notion that it was their duty to spread their beliefs and policies to other countries, in an effort to "help" these countries. Missionaries were sent to spread Christianity. Unfortunately, the missionaries usually had a patronizing view of the people they were trying to "help".
Direct and indirect colonial rule were very popular among the western powers. Britain, France and Germany were especially eager to acquire colonies.
Protectorates were sometimes assigned. These were rulers who were local, but who nonetheless had to play by the rules of their European advisors.
Britain encouraged children to receive a "British" education, so that new generations of people would spread westernized culture. Britain also tried to bring what it considered "culture" and "modernization" to India.
In some areas, the western powers had a "sphere of influence", which referred to countries in which the western powers dominated trading and investments.