War in Superpower 2 is a very hands-off affair, with no tactical control over the battles as they play out. Combat in Superpower 2 decided by several factors, the technology level of the armies, the numerical strength, the unit composition, and the pure luck.
Technological level is determined by how much technology each army has researched, and then how many points they put into a vehicle. These points determine attributes such as the speed, stealth, and firepower of a weapon system. The trade-off is that units cost more to build and upkeep the more advanced they are.
Unit Types and composition are also important. Even if a massive army of highly trained infantry attacks a much smaller army of tanks, attack helicopters, attack aircraft and bombers, the infantry swarm will be annihilated. Units in Superpower 2 are more effective against different types of units. Fighters are highly effective against other aircraft but are terrible at destroying ground units. Bombers vice versa. A good mix of forces will often times carry the battle against a numerically superior army that is heavy on one or two types of units.
War itself is declared by a power against another power. Either by moving a unit onto another nations territory without an Alliance treaty, or by selecting the "Request War" treaty. Once war is declared, the two nations armies can enter combat by moving close to each other. If a unit is alone in the territory of another nation, and there are no defenders in that territory, the land will fall under the military control of the attacking nation. Political control will remain with the defender.
War is mostly fought on the land and sea, with air units being attached to land armies and almost never operating alone. In standard Superpower 2, units can launch amphibious invasions no matter how many enemy ships are near the invasion site, however in the steam version of Superpower 2 you need a capital ship (Destroyer or Carrier) to invade via the ocean. Other nations may enter the war on either side, quickly turning the tide of battle.
War is either ended when both nations agree to a peace, or one of the two starting nations completely annexes the other. Annexation is a declared treaty, and after six months all of the territories under military control of the attacking nation fall under the political control of the attacking nation. If all territories of the defender are annexed, that nation ceases to exist.
Be warned! Annexation lowers your Diplomatic Relations with all other countries. In some cases against high-aggression AI players, they will often declare war.