The crisis began on Sunday October 14, 1962 when a United States Air Force U-2
aircraft on a photoreconnaissance mission captured photographic evidence of
Soviet missile bases under construction in Cuba (examples below).  

The United States considered attacking Cuba via air and sea, and settled on a
military "quarantine" of Cuba. The confrontation ended on October 28, 1962,
when President Kennedy and U.N. Secretary-General U Thant reached a
public and secret agreement with Soviet premier Nikita Khrushchev. The
quarantine officially ended on November 20, 1962. 

The SS-4 "Sandal" intermediate range missile

  

The Lockheed U-2 intelligence aircraft

On Monday October 22, President Kennedy announced the discovery
of the missile installations to the public in a nationwide televised
address.