The Cold War was the result of post-World War II distrust between the Soviet Union and the west.
The roots of this distrust go back to the Russian Revolution. During the fight between communist and tsarist forces, the western powers sent support and soldiers to help the tsarists. When the communists finally achieved victory, they vowed never to forget this. In general the west continued to distrusted communist states ideologically and did what they could to isolate Russia internationally.
On the other hand communist Russia was not shy about interfering in the affairs of western nations. They sent foreign aide to socialist worker revolts in Britain, France and the U.S. prompting Red Scares throughout the 1900’s. By the time World War II broke out, both sides allied only as a means to defeat Germany, but neither really trusted the other. The Russians were upset that it took the other Allied nations so long to open up a second front against Germany, and blamed them for a majority of the losses they suffered during the fighting.
After World War II, the Soviet Union was devastated. No other country had lost more people. They had been invaded through their western frontier several times and decided it was time to prevent this from happening again. As postwar Europe began to rebuild, the Soviets made certain that nations sharing a border with them were friendly. Since they occupied most of these countries, it was simple to help “massage” the local communist party into power despite assurances they would allow “free and democratic” elections.
The formation of what became known as the Soviet Block and the West’s answer in the form of the NATO is seen by many historians as the beginning of the Cold War.