Reddit mentions of The Looting Machine: Warlords, Oligarchs, Corporations, Smugglers, and the Theft of Africa's Wealth

If you're serious about looking in to this, I strongly recommend reading this book.

It's a bidding process. Usually the government assigns exclusive rights to access those natural resources inside a given area to a private company, which pays the government for the rights to do so and often forms a joint partnership of a sort to share some of the profits with either the state or some domestic private companies.

In the ideal case, the government opens the given area up for competitive bid and then chooses the one which maximizes public value. Because the government doesn't have the capital (or capacity) to extract the resources competitively or via its own private sector, allowing a large multinational company with expertise to do it instead makes a lot of sense for both parties. The resource extraction is usually paid for by the company (especially infrastructure, such as rail lines, building towns, etc). The state then benefits from increased taxation and its profit share of the resource extraction. As this is the ideal case, the state would also do something to mitigate the so-called "dutch disease" resulting from this windfall. As a result, everyone ends up happy. The resources are extracted, some of the profits go back to the people, and domestic industry advances as spillovers propel growth.

In the more common case, at least in underdeveloped resource-rich countries such as DRC, big companies pay bribes to local officials to buy support for their bids, then do the extraction without much local benefit being seen (because the money went to politicians, and wasn't distributed). Several of the worst offenders of this type today are Israeli and Chinese, although if you go further back you'll see Exxon, BP, Rio Tinto, and other Western companies doing some really "interesting" stuff. Today, because US anti-bribery laws apply to all foreign activity done by any US company, they aren't doing the really dirty stuff anymore, generally speaking. Or if they are, they're doing it good enough to not be caught.

For the ultimate example of the dirty type, peruse this - https://en.wikipedia.org/wiki/Beny_Steinmetz. You might be interested in reading The Looting Machine, which I thought was fantastic. It focuses on Africa primarily and how foreign companies come in, swamp locals with money, and get filthy rich in the process.