At present, issues of sovereignty on the Moon are similar to that in Antarctica or the high seas--the place itself is considered international territory. A nation or corporation may own facilities there, but may not lay claim to land that they are not actually using. Ideally, some international non-commercial body will oversee the leasing of mining rights in the same way as other "international" resources such as radio transmission spectrum rights. Under such a system, a mining company will buy the rights to mine specific areas for a certain number of years (as opposed to outright purchase of eternal ownership of the land being mined).
