Explanation:
The war was fought differently on different fronts. Let's focus on Europe:
The Nazis used the "Blitzkrieg" (lightning war) to easily break down morale on their enemies and disable them before ground troops reached the region. You could also argue that Germany imposed a war on race (Jews, Roma, etc.) and used concentration camps- genocide- to purge those who were not of the "Aryan" race.
The allies- Britain did the heavy lifting for most of the war, France was occupied by the Nazis- used weapons, guerilla tactics, and planes to administer war. When they invaded Germany towards the end of the war, they sent in bombs to disable important supply lines and buildings.
Let's not forget about Russia! They were originally part of the Axis Alliance at the start of the war, but switched when Germany violated their agreement of promising not to attack them. When Russia joined the Allies, they helped turn the tide of the war.
Southeast Asia:
Japan fought the war by overtaking islands. They wanted to add to their growing empire, causing them to use lots of planes and naval warfare.
How did Japan and Germany lose?
Germany: The allies focused on obliterating the Nazi Regime before focusing on the Pacific front. Russia stormed Germany from the east, and the USA and Britain from the west (they started this on D-Day). The economic and human toll of holding a two-front war was too much for Germany. They had also made lots of tactical mistakes during the war, contributing to their downfall.
Japan: When the USA entered the war, General Douglas MacArthur developed "island hopping". Basically recapturing one occupied island at a time, focusing on the most important ones, until they reached the island of Japan. The theory was that if they took islands one at a time, eventually all the others will follow. The Japanese were a tough foe to fight, despite Germany's surrender, Japan continued the war effort. The Island Hopping worked, and as they drew nearer to Japan, President Truman decided that a ground invasion would be too costly due to the projected human and economic toll. Unfortunately, they dropped the first atomic bomb on Hiroshima. When Japan still wouldn't surrender, they dropped another one on Nagasaki.
