The Cold War was began by actions made by the leaders of the US and USSR on that time, Stalin and Truman.
Stalin actions make the impression on the West that he wanted to spread communism, but instead he wanted to take advantage of the fact that the Red Army had control of Eastern Europe after the defeat of Germany, and only create a sphere of influence over the nearby territory. To strengthen his sphere of influence, Stalin established a communist government in Poland, even though that there was another government in exile at London. And also Oder-Neisse, in Germany, was occupied by Soviet army without the approval if other world leaders.
Truman, as well, has a very big responsibility for starting the Cold War. A series of actions led Stalin to suspect that both the US and Britain wanted to destroy communism of at least not let it expand.
One was that they didn't told him about the atomic bomb. Another important one is that the Allies took too long in launching an attack on France, thus creating the Second Front, Stalin thought that this was done deliberately to leave all the pressure on the USSR. Roosevelt had been giving supplies to Russia and he had accepted the sphere of influence in Eastern Europe, but Truman rejected both.
On the Yalta conference Truman disagreed on the USSR having a naval base in the Mediterranean, Stalin sharing the occupation of Japan, and most important that there wouldn't be reparations. This last fact was a source of conflict because the Soviet Union had been shattered by war and wanted something in return.
The last action made by the US that threatened Stalin was the Marshall Aid policy. With this he wanted to increase his influence over Europe and stop...