What military strategy did the US and Allies use to infiltrate Europe?

I'm very intrigued with how D-Day worked and all, but I don't really understand the logistics and strategy they used. I mean the Germans/Italians had almost all of Europe and it astounds how they came up from that small part of France which was Omaha Beach and etc, and ended up taking all of Europe back. The Germans had the "up-hill" advantage and I really wanna know how the Allies were able to take down the Germans, esp. on the beaches.