Geez, so many odd answers here, but your question is interesting. Before the Internet, each airline had its own CRO (central reservations office) where hundreds of "res agents" staffed rows and rows of desks, each with a computer terminal tied directly into the CRS (central reservations system), which was a main-frame computer. All the large airlines had their own, and would sell computer space to the smaller carriers as well.
To communicate with customers and travel agents alike, the CRO had an ACDS (automatic call distribution system) that received incoming calls (often to an 800 number) and directed them to the next available agent, who would talk to the customer and create the reservation, quote fares, flight times, etc.
Now in the days before main frame computers (i.e. before about 1959), the telephone call the customer made was handled by an agent that manually had books and books of flight information, and to create a reservation, a card was created that went on a card-carrying conveyance system to the central registry there to be entered. Often times, confirmation calls had to be made between the customer and the airline.
I could go on and on, because...