So, for example, during the Cuban Missile Crisis, how were the activities surrounding the blockade communicated back to Kruschev?
Communications during the Cuban Missile Crisis is an interesting topics. Both sides suffered from a communication problem. While both sides used radio or microwaves signals bounced off the upper atmosphere could be used to sent messages to ships, the ability to sent messages from the radio towers to the Pentagon/Kremlin was still dependent on manually operated copper wire telephone exchanges. Its for this reason that while Kruschev ordered the hips to turn around the night of Kennedys broadcast it took several days for the info to react the Pentagon war planners.
For communication throughout history with navies for the early 20th and very late 19th century it was mainly through wireless/radio signals relayed across relay stations which either passed the message on or used the telegraph system. During the mid 19th century telegraph meant you could sent a message from a friendly port. Before that the only way would be to use small fast ships to carry messages around. For example it took 16 days for the news of Nelson's victory at Trafalgar to reach the Admiralty (though this does include 2 days of fast riding up from Cornwall).
Note however that this means that military commanders had a lot more power/independence on how they conducted their wars so this shouldn't be taken as there was a lot of command problems as often the top leaders commanded from the war zone rather than make home.