What are the legal basis of acquiring a territory?

To 'acquire' is the act of obtaining something which is not yet your own.

It is inadmissible to 'acquire' territory by war, offensive or defensive.

Citizens of a territory may not have voted, or even been able to vote for the regime in power when war was waged and under the UN Charter, people have a right to self determination. To this end, a State may only 'acquire' territory through legal annexation.

Legal annexation requires a referendum amongst the citizens of the territory being annexed. (see the US annexation of Texas)