The United States and Great Britain shared a common goal of defeating fascism both in Europe and in Asia. Those joint goals were first enumerated in the Atlantic Charter which called for self-determination of all peoples, equal access to raw materials, economic cooperation, freedom of the seas, and a new system of general security. There were differences in their ideas about how the war was to be prosecuted; Winston Churchill once commented that the only thing worse than fighting with allies was fighting without them. At the Casablanca conference, it was decided that the Allies would invade the "soft underbelly of Europe" by attacking Sicily and moving on to Italy.
While the United States and Britain were concerned with the defeat of Germany and Japan, and thereby fighting on both fronts, the Soviet Union was only interested in defeating Germany; in fact had Hitler not broken his word to Stalin by invading the Soviet Union, it is entirely likely that the Soviets would either have stayed out of the war or come in on the German side. Aside from defeating Germany, the Soviet goal was also territorial gains in Europe. Churchill had been concerned about allowing the Soviets to reach Berlin first; but was overruled by Roosevelt and Eisenhower. He was afraid that the Soviets would have an unfair advantage at the end of the war if they were allowed to capture large portions of German territory. Churchill's fears proved to be correct.
The Soviets only agreed to come into the war against Japan in meetings at Teheran and Cairo; but only after Germany was defeated. They did declare war on Japan after the Yalta Conference, and invaded Manchuria, but the war ended shortly thereafter with the bombing of Hiroshima and Nagasaki. There is substantial argument among historians that the United States used the Atomic Bomb to end the war quickly to prevent the Soviets from making large territorial gains in Asia.