This was a DBQ question from a couple of years ago for the AP US History exam. The main things to focus on are his speeches and efforts around 1954 to tamp down McCarthyism. His administration's decision to remove Jakobo Arbenz from power in Guatemala also signaled his desire to protect the Western Hemisphere with containment of communism. You could also include his aggressive spending on the military, especially in the area of nuclear weapons and missile technology.
One of the major things the Eisenhower Administration did was to try to build up the US nuclear arsenal. They felt that this would allow them to deter any expansion by the Soviets. Since Soviet expansion was a major fear, this would have been a way to allay those fears
I guess another thing would be all the civil defense stuff people were doing back then. This was meant to make people believe that a nuclear war would be survivable.
I am not sure that the Eisenhower administration that did much in way of allaying people's fears about Communism. While America appears at the end of the World War II as a superpower and with unprecedented economic progress, it was a nation that possessed fear about a Communist takeover of the world. The Red Scare of the 1950s did not do much to allay such fears. At the same time, governmental policy was guided by terms like "Containment" or "domino theory" and intervention to stop Communism. This rubbed off on the American public, who became increasingly convinced that failure to stop the spread of Communism would trade off with their own state of being in the world. Culture was increasingly present with the "fear of the other," becoming a part of the fears of Communism. Eisenhower guided the nation with a sense of calm, but the policies pursued were driven by the fears of Communism. The fear of Cuba and the covert activities to remove Castro from his position, as well as expanded use of the Central Intelligence Agency (CIA) in undeclared operations in Africa and South East Asia did not do much to dissolve the fears of the American people.