There were a number of important events in this period of the Cold War.
The most obvious of these was the Korean War. This war helped to cement in the minds of the West the idea that he communists were dedicated to expanding across the globe by any means necessary.
In 1954, the French were defeated by the Viet Minh and left Vietnam. This didn't have such a huge impact right at the time, but it led to US involvement in the Vietnam War.
In 1953 and 1954, the US supported coups in Iran and Guatemala. These coups showed that the US was going to be aggressive in its efforts to prevent the spread of communism.
Finally, there was the Soviet crushing of the Hungarian uprising in 1956. This showed that the Soviets were not going to let their satellite states have any real autonomy.