When the Second World War ended in 1945, the uneasy alliance between the Soviet Union and its allies began to unwind. When disagreements arose over what to do with the lands liberated from the Nazis, the Cold War began. The United States, the United Kingdom, and France wanted to create democratic nation-states. The Soviet Union, on the other hand, wanted to establish a communist buffer of puppet states between itself and the West. Depending on your point of view, you could blame either side's irreconcilable differences and their mutual mistrust for the breakdown of the former alliance.
In July of 1945, the stage was set for the Cold War at the Potsdam Conference. It was here that the United States, the United Kingdom, and the Soviet Union decided how Germany and the liberated countries would be administered. Soon after, Stalin established the puppet governments of the Eastern Bloc, which upset America's hopes of creating new democracies in the region. In March of 1946, Winston Churchill gave his famous "Iron Curtain" speech. From the point of view of the USSR, this speech represented the antagonistic intentions of the Americans and British and marked the end of whatever amicable relations remained.
In 1947, President Truman announced that the United States would take whatever actions it felt necessary to prevent the further spread of communism around the world. This is known as the Truman Doctrine. That same year, the United States implemented the Marshall Plan. This ambitious project quickly rebuilt post-war western Europe with the intention of making it safe for democracy and less susceptible to Soviet influence.
The first international crisis of the Cold War began in 1948 when the Soviet Union blockaded West Berlin. This resulted in the Berlin Airlift and a renewal in militarization in the United States.
In August of 1949, the Soviet Union conducted its first atomic bomb test. This completely changed Cold War policy, as it introduced the possibility of mutually-assured destruction if the USSR and the USA went to war. As a result, several proxy wars were fought, including the Korean War, which began in 1950.