Truman emerged as president in 1945, at a time when the Allies had all but won the war. Germany surrendered to the Allies shortly after, but the Japan had not surrendered. As an alternative to an Allied landing on Japan, the USA dropped atomic bombs instead. Then the Japanese also surrendered. U.S. and USSR relations deteriorated in the postwar era as both Truman and Stalin became increasingly weary of their former allies.
At the Potsdam Conference Truman, Atlee and Stalin met to discuss postwar Europe. Truman had already grown increasingly suspicious of Soviet policies in Eastern Europe. The promised elections in the east had not transpired as the Allies had proposed at the Yalta Conference. Communist regimes had now began to emerge in the likes of Poland, Hungary, Romania etc, which brought friction between East and West.
As such, by 1946 U.S. and USSR relations were strained. Churchill's "Iron Curtain" speech in 1946 spoke of the new Eastern Bloc that had emerged in Eastern Europe, and called on further Anglo-American military co-operation. This speech did little to ease the surfacing Cold War.
Consequently, Truman began a shift in U.S. policy. As the Greek Civil War continued the Royalists requested support from the U.S., particularly as Britain could no longer meet their defense commitments in Greece. To this extent, the president agreed to grant the Greeks military aid in their civil war with Communist groups. Truman's new policy of containment would be extended beyond Greece, and became known as the Truman Doctrine. The Truman Doctrine offered U.S. military support to countries that could potentially see the rise of Communist regimes such as Greece and Turkey in the 1940s.
To assist postwar reconstruction in Europe, the USA also extended Marshal Aid. However, the USSR did not accept this policy; so Marshall Aid was provided only for Western Europe.
To stop aid reaching West Berlin, the Soviets blockaded the city in 1948. Truman and the West circumvented the blockade with an airlift. The blockade was eventually lifted by 1949.
President Truman continued in office with re-election during 1948. The relative victories in the Cold War had seen the Berlin blockade lifted, Marshal Aid bring postwar recovery and both Turkey and Greece victorious against Communist groups.
However, Korea in 1950 would see the Cold War escalate. As the North Koreans pushed the South Korean army back Truman gained support for U.S. and NATO intervention in Korea. With such support the NATO armies were able to push the North Koreans back to the 38th parallel.
Despite such victories, Korea would ultimately end Truman's time as president. Increased Chinese involvement slowed NATO's advances and ultimately halted them at the 38th parallel. Disagreements with MacArthur followed regarding further U.S. military actions in Korea, with MacArthur suggesting that the U.S. bomb Chinese supply points. However, Truman was weary of such proposals that could further escalate the war and dismissed MacArthur.
MacArthur was an U.S. hero, and the U.S. was more sympathetic with MacArthur. As such, as casualties also mounted in Korea support for Truman began to decrease. With little chance of a further term Truman duly left office in 1952.
Overall, Truman had done little to enhance U.S. and USSR relations during his period in office; and in fact they declined. However, in light of Stalin's evident breaches of the Yalta Conference the shift in U.S. policy was perhaps understandable. At any rate, the Truman Doctrine had gone some way to assisting the Greeks and Turks against Communist groups during the '40s, and saved South Korea in the Korean War. Likewise, Marshal Aid also assisted with postwar recovery in Europe. It should also be noted that the Korean ceasefire that followed in 1953 may not have happened if Truman had supported all MacArthur's military plans. As such, in the Cold War Truman's policies had won victories and prevented the rise of further Communist groups.