Three ways.
Dejure control of the moon:
The price would be whatever lobbying/bribes/incentives would be necessary to overturn the 1967 Outer Space Treaty and giving you sole proprietorship, while not having the people who over turned it getting replaced by people who would immediately reverse their decision. I have no idea how much that would be but you would have to start with a really good reason for why handing over property rights to the moon is in everyone’s best interest.
Defacto control of the moon:
You need to have enough money to launch create a military installation on the moon that is sufficient to prevent anyone else from landing there. This would probably cost in the range of hundreds of billions of dollars.
Decretum control of the moon:
You can simply declare you own the moon. Until you or someone else sends another expedition there it makes no difference. If someone does send an expedition there then you will probably want to benevolently grant them free access to your property just to prevent the hassle of defending it through one of the two methods described above.