What are some areas of conflict during the Cold War, being as specific as possible?
It's a very large conflict/topic, covering nearly half a century and most of the world, so to round out the excellent post above, consider some of the other areas of conflict as well:
1) Nuclear arms race and proliferation -- The Soviets raced to develop their own bomb after the US did in 1945. By 1949, our monopoly on the weapon was over, and more countries soon followed, including Britain, France and China. Communist China and the USSR pointed their missiles at the West. The West pointed theirs towards the East. Both sides dumped trillions into these weapons, and by 1986, there were more than 28,000 of them worldwide.
2) Korea - Also known as the "Forgotten War" because historians refer to it so rarely, and most Americans don't remember it, this was a hot war purely related to the Cold War. Communist North Korea and China trying to expand into South Korea. The US and our allies in the UN trying to stop them. Over two million people were killed in the process with little change in the actual border.
3) Latin America - The US was very concerned about communism getting a foothold in the Western Hemisphere and used a mixture of foreign aid, CIA operations and assassinations to keep it from happening. The major flashpoint was Cuba and the 1961 Bay of Pigs and 1962 Cuban Missile Crisis, but there were also interventions in El Salvador, Bolivia, Chile and Nicaragua to try and keep those countries from going communist or to contain them if they did.
There were many areas of conflict (both geographical areas and "areas" like the economy and space) in which the United States and the Soviet Union competed in the Cold War.
For example, the Vietnam War was an area where proxy forces were used by one or both sides. The Americans first used the French as proxies while the Soviets used the Vietminh. Later on, the Americans were directly involved while the Soviets used North Vietnam as proxies.
Another example would be the Soviet invasion of Afghanistan. There, the USSR was directly involved while the US used the mujahideen as proxies.
A third example would be the space race. The Soviets won the first leg of this by getting Sputnik into orbit before the US orbtied anything. This gave the USSR great prestige. Later on, the US won the race to the moon and regained prestige.
These are different ways/areas in which the two sides came into conflict.
The Cold War began as World War II was ending. American leaders saw the power and ambitions of the Soviet Union as a threat to our national security. The Cold War was a war of words and ideologies rather than a shooting war, although at times the Cold War turned “hot” as in Korea and Vietnam. Basically, the Cold War was a rivalry between the United States as leader of the western democracies, and the Soviet Union and the nations that were controlled by the communists. Some causes of the Cold War included: Attempts by the Soviets and Chinese Communists to influence and take over areas in Asia and Europe. Containment--the policy of the United States to stop communism from spreading to other areas of the world. The Truman Doctrine--a policy of supporting anti-communist regimes with military and economic aid. The Doctrine was first used in support of democratic governments in Greece and Turkey. The Marshall Plan--a massive plan to aid in rebuilding Europe after World War II. Western allied nations, as well as neutral nations, and even the Soviet Union were offered economic assistance. The Soviet Union saw this as a threat to their attempt to gain influence in Europe and Asia. The division of Germany after the war---The Soviets blockaded West Berlin, which was deep within Communist East Germany. The Soviets thought the blockade would allow them to take over all of Berlin. The US replied with the Berlin Airlift, to supply West Berlin. The North Atlantic Treaty Organization (NATO) was formed in 1949 by the US, Canada, and nine European nations, the first peacetime military alliance in US History. The NATO nations agreed that an attack on one would be an attack on all. The Soviets replied with the Warsaw Pact, a military alliance of communist nations in Eastern Europe. September, 1949, the Soviet Union tested its first Atomic Bomb. The Cold War continued through the decades of the 50s, 60s, 70s, and 80s, until the collapse of the Soviet Union and the fall of the Berlin Wall