conflict wished to risk a nuclear war. This is exactly whatprobably would have happened if the Soviets had invaded Western Europe. The Soviet invasions of 1956 in Hungary and 1968 in Czechoslovakia were attempts to rein in governments that were already part of the communist bloc (going back to the end of World War II) and which the Soviets believed had become too liberal. Therefore, during the Cold War, direct Soviet expansion into areas not already in their sphere of influence was never attempted in that most crucial geopolitical realm, the European continent.

What would have happened eventually if the Soviets had not suffered an internal collapse, no one has any way of knowing. By the 1980's, the Soviet Union found itself in a quagmire in Afghanistan, partly because of aid the US was giving to the Afghan resistance. During the same period, the open defiance of the Solidarity Union in Poland, as well as internal dissent by the refuseniks within the Soviet Union itself, showed that the regime lacked either the will or the ability to crush these efforts. Much credit has been given to the Reagan administration's buildup of weaponry during the same period. The Soviets could not keep up with this arms race, and their attempts to do so contributed to the failure of their economy. So, the decisive areas in which US involvement led to the failure of Communism to expand and to the eventual demise of the Soviet state were the support given to the Afghan rebels and the acceleration of the arms race.

Those who supported US involvement in Vietnam asserted that the US effort there, though it eventually failed, was what nevertheless deterred additional attempts by the Soviets (and the Chinese) to expand and to conquer additional countries. But this theory is speculative at best. One can far more credibly claim that the U.S. failure in Vietnam would have encouraged further communist attempts to take over other countries, if this was indeed their goal.

The answer above does a good job outlining U.S. efforts to contain communism in the years just after World War II. This effort has continued. 

The U.S worried about what was called domino effect. It was feared if one country in a region went communist, surrounding countries would follow. For this reason, the U.S. used its military might to prevent that. The U.S., for example, got involved in a costly war in Viet Nam because it feared if that country went communist,  communism would spread throughout Southeast Asia. While that military action did not go well for the U.S., some argue it was a success because communism did not advance throughout the region.

The U.S. considers the Western hemisphere, including South America, as in its sphere of influence. It has backed military coups and rightwing dictatorships in Latin American countries to contain the spread of communism there. While some have complained of U.S. methods, these methods have been effective: this hemisphere has remained largely free of communism. 

The U.S. also used propaganda to argue for the superiority of the democratic system of government, sponsoring Radio Free Europe to deliver its message to the communist satellite states. The U.S. also used the Agency for International Development to bring aid programs to countries it feared might go communist. 

After World War II ended, the United States and the Soviet Union opposed each other in many places, often dealing with the spread of communism. The Soviet Union wanted to spread communism, and we wanted to keep it from spreading.

The United States developed a policy called containment to stop communism from spreading. The basis of this policy was that communism would fail, and we needed to just keep communism from spreading. One example of containment in action was the development of the European Recovery Plan, also called the Marshall Plan, where we offered economic aid to European countries trying to prevent communism from spreading to their country. We knew that countries with a strong economy were less likely to become communist. For example, the economic aid helped keep Greece and Turkey from becoming communist.

We also came to the aid of West Berlin. When the Soviet Union cut off all land routes to West Berlin in order to force the Americans, British, and French to abandon the city, we organized the Berlin Airlift. We flew supplies into West Berlin until the Soviet Union lifted the blockade.

When North Korea invaded South Korea in 1950, we went to the United Nations for action. North Korea, unprovoked, invaded South Korea in June 1950 in order to unite Korea into one country that would be communist. The United Nations, led by the United States, helped South Korea fight North Korea. North Korea was not able to conquer South Korea and make it communist.

The United States also developed a military alliance to deal with the spread of communism. The North Atlantic Treaty Organization, or NATO for short, was a military alliance including the United States and many of the noncommunist nations of Western Europe. This alliance formed in case there was a conflict with the Soviet Union.

There were several actions the United States took after World War II ended to stop communism from spreading.