When can a person or country stake claim to land on another planet? At what legal point can a country declare we own this land in the name of whom so ever?
Currently it is not supposed to be done in space. There's a UN Resolution titled Declaration of Legal Principles Governing the Activities of States in the Exploration and Use of Outer Space which was adopted unanimously in 1962 which includes this statement:
Outer space and celestial bodies are not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.
Consider also the Antarctic Treaty System, which states that no new territorial claims in the Antarctic may be established while the treaty is in force. There remain some disputes in the Arctic however, for example a somewhat whimsical one over Hans Island.