We won..
Well, that answer is almost simple. But everyone, including historians, have different opinions.
What I've always been taught in school:
European Theater:
Germany was allied with Russia for a while, meaning they only had one front to fight the war on. They could easily concentrate troops there and didn't have to defend/leave many troops in other areas. They just had to have enough to occupy diminished countries. The second they invaded Russia, they suddenly had two fronts to fight on, and all their forces became divided. Then suddenly they had a crushing force shoot in from Normandy and paradropped in, and they became more or less overwhelmed. Once Hitler commit suicide, they were toast. Happy VE Day.
Pacific:
Let's face it, we won because of the atomic bomb. There's no contradicting that. Japan wasn't winning, but neither were we. We won because we had the best minds in science come together and form this insane project to create atomic bombs. Japan had been working on the same thing, and a sciencist locked in a German-occupied area was responsible for the main discovery of what substance to use in the atom bomb that wouldn't diminish quickly, and we snuck his documents out via special force paratroopers. Then, baddabing baddaBOOOOM. Bomb dropped, Japan announces it's surrender. Happy VJ Day.
Resources:
Books:
Hiroshima, John Hersey
Brighter Than a Thousand Suns, Robert Jungk
Los Alamos, LASL Public Relations Staff
The Making of the Atomic Bomb, Richard Rhodes