It very much depends on what sort of colonialism you're talking about, as it came in many forms which functioned rather differently. Its broadly accurate to say that these forms almost invariably involved 'theft' of indigenous wealth and its transfer to Europeans, though the way in which this occurred varied from actual theft of physical wealth to exploitation of indigenous labour/land, or a mix of both.

In the case of the Spanish Empire, for example, they quite literally did plunder gold from Central and South America and bring it back to Europe. Spanish colonies also made money through a system of slavery known as encomienda, where indigenous people were forced to work on behalf of the conquistadors who had conquered them.

The English colonies in the Americas made money in different ways, such as growing sugar and cotton on plantations worked by slaves, on land either purchased or taken by force from indigenous people. French colonies in Canada were often focused on the fur trade. Some of the more northern English colonies where there was no sugar or cotton industry were often not really very profitable in their early stages. Instead, they were maintained either for strategic reasons and national prestige, or by colonists who operated with a degree of independence from the crown and were motivated often by religious considerations, such as the Rhode Island or Pennsylvania colonies.

In Asia, things worked differently again, with groups like the Portuguese and Dutch operating 'factories'- trading posts for things like spices, slaves, and cloth, often fortified and established by force. This sort of empire arguably operated on the basis of a mixture of reciprocal trading, threats, extortion, and outright conquest or plunder.

I'm not really very familiar with the details of how the British Empire in India functioned, so hopefully somebody else might be able to say more about that.