The two most important new aspects of warfare seen in this war were blitzkrieg and strategic bombing.
Blitzkrieg was an idea pioneered by the Germans early in the war. It was based on being able to move troops rapidly from place to place (by motor vehicle or even by airplane in the case of paratroopers) and on very good coordination between tanks, infantry, air support, artillery. The Allies used this type of warfare later in the war as well.
Strategic bombing was done by using large waves of bombers to hit targets like factories and railroad yards rather than just bombing troops and other military targets. The Americans and British used this against Germany very effectively. The Americans used captured islands as bases from which to launch strategic bombers against Japan. This type of bombing hurt the German and Japanese efforts to keep their war machines supplied.