Kennedy's Foreign Policy was centered on competing with the Soviet Union and to maintain the long standing policy of containment. However, he was reluctant to engage the Soviets militarily (which caused friction between him and his military staff). In his short term in office (about 2 1/2 years), he was faced with some of the most challenging events of any President.
The Bay of Pigs - the CIA led invasion of Cuba intended to remove Fidel Castro from power. It was a complete failure and a complete victory for the Soviet Union. Kennedy did not trust the CIA after this mission and shifted his cabinet. He fired CIA director John Foster Dulles and replaced him with John McClone. He did not accept advice from the CIA and instead, trusted his brother and closest advisor, Robert Kennedy, the Attorney General.
The Berlin Airlift - The Soviet Union wanted to stop defections to the democratic west. They started to build a wall that separated East and West Berlin, Germany. The US could not stop that action but they could show support to the people of Berlin by airlifting supplies to the residents of Berlin (both East and West). The significance here is that the US would respond to any Soviet action in any part of the world.
The Cuban Missile Crisis - was the most challenging event of the Kennedy administration. The Russians were putting nuclear weapons in Cuba which is only 90 miles from the US mainland. This is a direct violation of the Monroe Doctrine and long standing US policy of no European involvement in the Western Hemisphere. The US went to the brink of war over Cuba in October of 1962 but the Russians backed down and removed the missiles.