In most countries anything culturally significant or historic or valuable past a certain amount, goes to the government. Sometimes there is a reward that the museums or gov will give to the person who found it but it's rare that if you found a treasure it's yours, and rare to get a large cut. In many countries you have to report any finds within a certain amount of time.

On private land sometimes it's a deal you make with the landowner before you have permission to scout the land.

A lot of people just don't report their finds and sell them through a black market, or just keep them as souvenirs and don't sell them or notify anyone.