The United States did many things that could be seen as attempts to combat the spread of communism and to make itself into a hegemonic power in the world. Let us look at four general types of things the US did.
Military actions. In these cases, the US used military force to try to prevent the spread of communism. There were times, such as the Korean War, when this was successful. However, there were also times, as with the Vietnam War, when the US failed.
Economic actions. The US typically tried to use economic aid to bolster its allies. By helping these allies economically, the US hoped to strengthen the allies’ economies and make them less susceptible to succumbing to communism. Perhaps the best example of this was the Marshall Plan.
Social actions. The US tried to project what is known as “soft power” around the world. This essentially involved doing things to try to get other countries to think well of the US. One major example of this was the Peace Corps.
Political actions. The US also acted politically to prevent the spread of communism. For example, it created blocs of countries that were supposed to help one another resist the spread of communism. The major example of this is the creation of NATO.
In these ways and others, the US tried to prevent the spread of communism during the Cold War era. One can argue that these efforts also tended to make the US a hegemonic power.