When the United States entered the war in December of 1941, the war in Europe was going very badly for the Allies. The war in the Pacific had pretty much just started, but it was not going well either.
In Europe, Germany had conquered essentially all of Europe. There were a few countries on the continent that were neutral, but none left that were hostile to Germany except for the USSR. And at that point, the German army was occupying most of the European part of the USSR.
So, at the time the US entered the war, things looked very bad for the allies.
As for how the war was won, you've asked some questions (like about the strategy) that answer that.