At 5:00 pm, [October 22, 1962, President Kennedy] met with Congressional leaders who contentiously opposed a blockade [of Cuba] and demanded a stronger response. In Moscow, Ambassador Kohler briefed Chairman Khrushchev on the pending blockade and Kennedy's speech to the nation. Ambassadors around the world gave advance notice to non-Eastern Bloc leaders. Before the speech, US delegations met with Canadian Prime Minister John Diefenbaker, British Prime Minister Harold Macmillan, West German Chancellor Konrad Adenauer, and French President Charles de Gaulle to brief them on the US intelligence and their proposed response. All were supportive of the US position.
On October 22 at 7:00 pm EDT, President Kennedy delivered a nation-wide televised address on all of the major networks announcing the discovery of the missiles.
It shall be the policy of this nation to regard any nuclear missile launched from Cuba against any nation in the Western Hemisphere as an attack by the Soviet Union on the United States, requiring a full retaliatory response upon the Soviet Union.
Kennedy described the administration's plan:
To halt this offensive buildup, a strict quarantine on all offensive military equipment under shipment to Cuba is being initiated. All ships of any kind bound for Cuba, from whatever nation or port, will, if found to contain cargoes of offensive weapons, be turned back. This quarantine will be extended, if needed, to other types of cargo and carriers. We are not at this time, however, denying the necessities of life as the Soviets attempted to do in their Berlin blockade of 1948.
During the speech a directive went out to all US forces worldwide placing them on DEFCON 3. The heavy cruiser USS Newport News was designated flagship for the blockade, with the USS Leary (DD-879) as Newport News' destroyer escort.
Here is a You Tube post of that fateful speech.