Who would actually get paid if the US bought Greenland?

Greenland is back in the news. While this likely will never happen, who actually gets paid if it did? How does it work when countries get bought in general? Who 'owns' a country?

Let's say we buy Greenland for 1 trillion dollars. The money goes to Greenland, but now we own Greenland, so now where does the money actually *go*?