You make money first by creating the tangible / intangible artifacts of that exchange, like currency, systems of accounting, and such. You then get other people to use the system to exchange goods and services.
This typically requires a government, but other entities have made money in the past, and even today. Bitcoin satisfies all the criteria of money.
The practice of fractional-reserve banking is another example of money creation. Most banks will lend out more money than they have access to in deposits, as a relatively safe form of leverage.
This has the effect of slightly expanding how much money is available to the economy, aggregated over all the banks and loans being made by those banks, the expansion is significant.
Things like video game currencies also satisfy all the criteria of money, though the things you can buy with them are limited, sometimes you can trade them for other currencies.
So there's lots of ways to make money.