How did the leaders cause the Cold War and, specifically, how can you link them with the events from 1945-1963?
Leaders can be said to have caused the Cold War to start and to continue. The start of the Cold War, for example, can be attributed to Stalin. By taking the countries of Eastern Europe and dominating them, Stalin caused the West to fear him, thus helping to start the Cold War. Alternatively, one could blame the start of the Cold War on Truman. One could say that his Truman Doctrine pledged the West to resisting communism and created an adversarial relationship between the two superpowers.
Later events can also be blamed on the leaders. It was Stalin who ordered the Berlin blockade. It was Khrushchev who decided to put missiles in Cuba. It was Kennedy who approved the invasion at the Bay of Pigs. All of these actions helped to sustain the Cold War during the time period that you are asking about.