Short answers, pulled from the story.
The Prague Spring began on the 5th of January 1968, when Alexander Dubček was elected First Secretary of the Communist Party of Czechoslovakia, and ended on the 21st of August 1968, when Soviet Union and four other Warsaw Pact members invaded the country.
On the night of the 20th of August 1968, 165,000 troops and 4,600 tanks entered Czechoslovakia in the initial assault. The New York Times cited reports of a total of 650,000 men equipped with the most modern Soviet military weapons.
Jan Palach was a Czech student who set himself on fire in Wenceslas Square on the 16th of January 1969 to protest the renewed suppression of free speech following the Soviet invasion. He became the most famous of several protest suicides by self-immolation and is memorialized at the site, which is often called the "boulevard of history".
The Brezhnev Doctrine was the Soviet policy of using military force to compel Warsaw Pact satellite states to subordinate their national interests to the Eastern Bloc. It was used to justify the August 1968 invasion of Czechoslovakia, and China's Mao Zedong viewed it as a potential ideological basis for a Soviet invasion of China as well.
Dubček was arrested on the night of the invasion and taken to Moscow, where he signed the Moscow Protocol under heavy psychological pressure. He was replaced as First Secretary by Gustáv Husák in April 1969 and expelled from the KSČ, then assigned work as a forestry official. He later supported the Velvet Revolution of December 1989 and became chairman of the federal assembly before his death in November 1992.
Milan Kundera set his novel The Unbearable Lightness of Being during the Prague Spring, and a film version was released in 1988. Karel Husa composed Music for Prague 1968, and Tom Stoppard's play Rock 'n' Roll also references the events. The number 68 became iconic in the former Czechoslovakia, adopted by hockey player Jaromír Jágr and taken as the name of a Toronto publishing house for exiled Czech and Slovak authors.