In a sense, the Cold War was inevitable from the time that the Bolsheviks prevailed in the Russian Civil War. Their ideology and the capitalist/democratic ideology of the West were simply incompatible. While this was the basic underlying cause of the Cold War, there were more immediate causes that came out of World War II.
The basic cause of the Cold War was the communist ideology espoused by the Bolsheviks. They believed that history was leading inexorably to the triumph of communism. They believed that communism would come to exist everywhere in the world. Most importantly, they believed that they should help to make this happen. Because of this, there was a fundamental tension between them and the capitalist countries of the West.
WWII caused those tensions to manifest themselves in the Cold War. The Soviets had been traumatized by the experience of invasion from the west (just as they had been in 1812 when Napoleon invaded). They felt that they needed a buffer zone between themselves and the West to prevent future invasions. This led them to want to have control over Eastern Europe. As the Soviets took control of Eastern Europe, the West became concerned as they felt that this was the beginning of a Soviet attempt to spread communism across the entire world.
Thus, the fundamental incompatibility of capitalism and communism and the stresses caused by WWII were the major causes of the Cold War.