Returning from a trip to Chicago, stating that he had a cold, the President discussed options and next steps with his advisors. Then he told the country, on the 20th of October, 1962, that he had "unmistakable evidence" which showed Soviet offensive missiles were being installed in Cuba.
He also made clear something else: "It shall be the policy of this nation" that any attack on any western-hemisphere country would be considered an attack on America. The seriousness of the speech, and the crisis, put the whole world on edge.
After placing American military forces on higher alert - DEFCON Three - the President needed more information. Another U-2 spy plane flew to Cuba. He flew so low that people on the ground could see his face.
President Kennedy considered various options, including an invasion of Cuba. He had no idea, however, that if he had sent an invasion force to Cuba, his troops would have faced a nuclear response.
Clip from DEFCON-2: Standing on the Brink of Nuclear War During the Cuban Missile Crisis, a Discovery-Channel documentary (hosted by Tom Clancy) including interviews, historical footage and recreated scenes, produced to commemorate the 40th anniversary of the Missile Crisis.