The major Allied strategy during this time was to fight around the periphery of Europe while trying to weaken Germany and build Allied strength. Once this process was complete, the Western Allies could mount an invasion of Western Europe and attack Germany directly.
Early in WWII, the Germans were simply too strong and the Allies were too weak since America's industrial might had not fully been activated. Therefore, the Allies had to try to nibble away at Germany in places like North Africa and, eventually, Italy. As they did this, they also conducted strategic bombing of Germany to try to weaken its ability to produce and move war materiel. After a few years of this build up, the Allies felt strong enough to mount the D-Day invasion of Europe.