Sending an Email in 1984 [video]
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Without a computer of your own, using only a dumb terminal and at the minimum an acoustic-coupled telephone modem, you dialed a regular telephone number which would be answered only by the modulated tones of the target time-sharing system.
Your modem decodes the incoming tones to text on your terminal (CRT and/or Printing) in real time, a lot of terminals were so dumb they had no significant memory or scrollback at all. And it was just fine.
You signed on to your particular email server, picked which message to read and looked at the text as expected, printing optional.
To send you entered compose mode, typed your message into the terminal, indicated recipients and away it goes.
Now if you had a computer you could still "get by" with the same old acoustic modem (even using a rotary dial telephone manually without "touch-tone" service from AT&T), but you were still going to need to run a terminal program. So your personal computer would then emulate the above "console" where the COM port is directly interfaced with the keyboard and screen for this purpose, usually a "smart terminal" where you could also send & receive text which you have stored locally (in the form of text files), beyond simply reading & sending text with no local storage other than printing. Plus these were not dumb terminals these were computers so it could be good to attach files that are not text at all. Naturally you would need to make sure you had enough available space on the proper floppy disk for that ;)
When hypertext started to be experimented with, if you had an "interpreter" it would respond to the tags and display the formatted output. With only a "filter" it would remove the tags so you could read the plain text easier, and if you still had a dumb terminal at least every bit of content was there even if the tags were scattered all about among the plain text.