How did the conclusion of World War II lead to the events of the Cold War?

The Soviets fought in World War II as allies of the British and Americans (after the Soviets' Non-Aggression Pact with Nazi Germany collapsed in 1941), but there was growing mistrust between the Soviets and the western allies during the war. During the war, the Soviet leader, Stalin, had annexed several countries bordering the Soviet Union, including Estonia, Latvia, eastern Poland, Romania, and Lithuania, according to the terms of the Molotov-Ribbentrop Pact with the Nazis. After the allies defeated the Nazis in May of 1945, the Soviets effectively occupied many countries in Eastern and Central Europe, including the Baltic states, Poland, Hungary, Czechoslovakia, and others. Stalin maintained that occupation of these areas was necessary for the defense of his country. 

While the allied leaders, Stalin of the Soviet Union, Franklin D. Roosevelt (FDR) of the United States, and Churchill of Great Britain, met several times, they failed to reach a consensus. At the Yalta conference in February of 1945, Stalin, Churchill, and FDR failed to reach an agreement about the division of post-war Europe, and the distrust grew. At the Potsdam Conference in July of 1945, tensions ran high. After FDR's death, Truman, who had largely been kept out of foreign affairs as FDR's Vice President, had become President, and he was planning to drop the atomic bombs on Japan. He shared this news with Stalin, who was apparently not surprised (as he may have been informed of the American nuclear plan through spies). The detonation of the bombs over Hiroshima and Nagasaki in August of 1945 further worsened the Soviet distrust of Americans. In addition, the allies decided to divide Germany into four zones: one French, one British, one American, and one Soviet. However, over time, disagreement about the payment of German reparations and other issues led the allied sector to break off from the Soviet sector. Over time, the allied sector became West Germany in 1949, followed by the creation of East Germany the same year. The Cold War accelerated at the end of the 1940s and into the 1950s and beyond.