The Allies defeated Germany by the US and Britain sitting back and letting the Soviet Union do all the really bloody work. For much of the war, the US and Britain were only really fighting German in the air and on the sea. During that time, the Russians were losing huge numbers of men fighting Germany on the ground and weakening Germany considerably.
The Western Allies put some pressure on Germany by invading Northern Africa and then Italy, but the main ground fighting was still on the Eastern Front. When D-Day came, Germany was finally forced to fight a two front war and quickly lost.
So the strategy was for the US and Britain to attack Germany's industrial capacity while the US built up the Allied arsenal. As they did this, the Soviets did most of the fighting and dying. When the arsenal was built up enough, the Western Allies invaded Europe and dealt the death blow to Germany.
The Allies defeated Germany in part because they had more resources, particularly after the United States entered the war in late 1941. After that point, the tide of the war began to shift in the Allies' favor. In the Pacific Theater, the Allies used Hawaii and Australia as launching points for their strategy of "island hopping" or "leap frogging," which involved attacking less defended islands in the Pacific en route to approaching mainland Japan. The Battle of Midway in June of 1942 was the first important Allied victory on the way to ever-closer attacks on Japan. The war culminated first with incendiary bombing over Japanese cities and then with the detonation of two atomic bombs in August of 1945, leading to Japanese capitulation.
In the Western Front in Europe, the Allies began with an assault on German troops in North Africa in 1942. Led by American general Eisenhower, the attack, which included forces from Britain, New Zealand, and Australia, was successful, and from there, the Allies headed to Sicily and up the Italian boot, meeting with fierce German resistance. At the same time, the Allies conducted heavy bombing over German cities such as Dresden. On the Eastern Front, the Russians repelled a German invasion, incurring heavy military and civilian losses. The Allies launched an amphibious attack on Normandy in France during D-Day in June of 1944 and, from there, fought their way to Berlin, where the Soviets met them in the final days of the war. In the end, the Allied manpower and resources overwhelmed those of Germany, Japan, and the other Axis powers.
the allies defeated the Germany and the Japanese by dropping two atomic bombs