What triggered the crisis was our deployment of missiles to Turkey. We refused to remove our missiles so they decided to deploy missiles to Cuba.
We saw them building the launch facilities and warned them we would go to war if they sent missiles to go in those silos. They said fuck you, and shipped the missiles.
Kennedy declared an interdiction of the waters around Cuba. He called up the Naval Reserves (my dad had to go for 7 months he was bitter about it) and deployed the Navy to search EVERY SINGLE vessel going to Cuba.
The Soviet missiles kept getting closer and closer. The world held it's breath. Would we attack the Soviet missile ships. Would a nuclear war break out?
Khrushchev called a meeting of the Politburo, pounded on the table with his shoe. Told them there was no way he was going to kill his grandchildren over this. Had a few people and generals hustled out and shot.
Then called the ships back.
Just before his death Kennedy had our missiles removed from Turkey. The advantage they gave us in terms of "sudden strike without warning" capability wasn't worth the destabilization it caused.