Short answers, pulled from the story.
The Warsaw Pact invasion of Czechoslovakia began at approximately 11 pm on the 20th of August 1968 and continued into the 21st of August. Four countries participated: the Soviet Union, Poland, Bulgaria, and Hungary.
The Prague Spring was a period of political liberalization in Czechoslovakia that began on the 5th of January 1968 when Alexander Dubček became First Secretary of the Communist Party. Dubček's reforms, which included abolishing censorship, expanding freedom of speech and movement, and planning a mixed economy, alarmed Soviet and Warsaw Pact leaders who feared Czechoslovakia might defect from the Eastern Bloc and that liberalization would spread to Poland, East Germany, and the Soviet republics.
About 250,000 Warsaw Pact troops and 2,000 tanks crossed the border on the night of the invasion, with the total eventually rising to 500,000 troops. During the occupation, 137 Czechoslovaks were killed and 500 seriously wounded.
Romania and Albania refused to participate in the invasion. Albania subsequently withdrew from the Warsaw Pact entirely in September 1968. East Germany's National People's Army was also excluded at the last moment, at the request of Czechoslovak opponents of Dubček who feared greater resistance if German troops were present, given the memory of the German occupation thirty years earlier.
Dubček was arrested by the KGB on the night of the 20th of August 1968 and flown to Moscow, where he was held in secret and interrogated. He was returned to Prague on the 27th of August and initially retained his post as First Secretary. He was forced to resign in April 1969 following the Czechoslovak Hockey Riots, and was replaced by Gustáv Husák.
The Brezhnev Doctrine was the Soviet policy of compelling Warsaw Pact satellite states to subordinate their national interests to those of the Eastern Bloc through military force if necessary. It emerged directly from the 1968 invasion of Czechoslovakia and was used to justify Soviet intervention whenever a communist government was deemed insufficiently aligned with Moscow.