Three successive US presidents have erected, through the force of precedent, an incontestable power to kill whomever the president pleases, and a power to wage war wherever the president chooses. From Philip Giraldi at strategic-culture.org:
Once upon a time there was a Constitution of the United States. In Article II, Section 2 it stipulated that only the U.S. Congress has the power to declare war, which means the American president has to go to the legislative body and make a case for going to war against an enemy or enemies. If there is a vote in favor of war, the president is empowered as commander-in-chief to direct the available resources against the enemy.
There is also something called international law. Under international law there are situations in which a head of state or head of government can use military force defensively or even preemptively if there is a substantial threat that is imminent. But normally, a country has to go through a procedure similar to that in the U.S. Constitution, which means making a case that the war is justified before declaring war. The Nuremberg Tribunals ruled that starting a war of aggression is the ultimate crime.