How would a government legally take control of another territory to add to its own

A government can legally take control of another territory by CESSION

Explanation:

Cession is the surrender or assignment of a territory under the control of a country or state to another country or state. this done as a repayment of debt been owed or as a former of surrender or as part of a peace treaty. cession is documented legally and agreed to by both parties i.e the country giving up its territory and the country/state receiving it. Example is the cession of New mexico to the USA by Mexico after the war

Annexation is also a means of taking another territory by a country. this is mostly done through Military invasions and hence it is not a legal means  example of such is the Nazi Germany annexing Austria through military invasion.

salmon were fished in puget sound.

it is a : ) always outside of government control