This was a hard question to find a quick answer to. From what I can tell from a brief online search, the first online program was started by the Western Behavioral Sciences Institute (specifically in the School of Management and Strategic Studies) in 1981 (http://www.worldwidelearn.com/education-articles/history-of-distance-learning.html, http://en.wikipedia.org/wiki/Western_Behavioral_Sciences_Institute).
What did this program look like? Well, here it is described generally:
The equipment was expensive and primitive. We used Apple IIE’s with 48K of memory and 300 baud modems. (Multiply by 1000 and 100 respectively to get current averages.) The complexity of basic computer operations in those days was such that it took a full page of printed instructions just to connect. A variant of email called computer conferencing was the only available electronic mediation.
Computer conferencing was suited to our application since it facilitated the sort of many-to-many communication that goes on in the classroom, but no one knew how to use it for education. None of us had ever been a student in an online class or seen one in operation, and we did not know the answers to the most elementary pedagogical questions, such as how to start a class, how long or short messages should be, and how often the teacher should sign on and respond to the students. (http://www-rohan.sdsu.edu/faculty/feenberg/TELE3.HTM)
Targeting “high level executives who could not afford long absence from their jobs, the electronic delivery system provided these executives with an exciting initiation to computers through a communications application suited to their skills and interests.” (http://www-rohan.sdsu.edu/faculty/feenberg/wbsi3.htm) But, of course, there were some challenges:
The real problems began when the participants returned home [after the initial face to face meeting].  Since no one had ever been taught on a computer network before, there were no models. The first courses consisted either in professorial monologues that made interesting reading but were unsatisfactory as computer conferences, or telegraphic questions followed by days of inactivity while the teachers waited for responses. Meanwhile, various technical problems inhibited the participants from joining in the conversation, such as it was.…
WBSI’s first attempts at online teaching were disastrous. Great teachers were helpless in front of a class of sympathetic but sceptical students scattered between Caracas, Philadelphia and San Francisco. One teacher offered elaborate presentations that resembled written lectures. While interesting, these had the undesirable effect of reducing the participants to silence. In a face-to-face classroom teachers can determine from subtle clues whether students’ silence signifies fascination or daydreaming. But silence on a computer network is unfathomable; it is intensely disturbing to address the electronic void. Â (http://www-rohan.sdsu.edu/faculty/feenberg/wbsi3.htm)
I think we’ve come a long way since then (although some of the challenges remain the same)! But we might not be here now if it weren’t for those pre-Internet pioneers.
