Wikipedia, unsurprisingly, gives incomplete information. A number of important new technologies were developed as part of the five-year R&D of SABRE, including a disk drive capable of storing that many reservations, a new transaction-processing system, a frequency-modulation system to send data over the phone lines, and a new model of terminal, pictured here. It was a teletype with a keyboard that printed both results and tickets on paper. There were originally 1,500 of them.
A retrospective in Wired Magazine describes the workflow:
Take a tour of a SABRE console. The agent places a coded card with a list of flights to the destination airport to the right of the console's buttons. By pressing a "need" button, the agent queries SABRE's New York reservation center. The lights, located just right of the buttons, light up if the requested flight is unavailable. The agent uses the keyboard to enter the customer's name and personal information.
Teleprinters would be placed at American Airlines' ticketing offices to send in requests and receive responses directly, without the need for anyone on the other end of the phone. The number of available seats on the aircraft could be tracked automatically, and if a seat was available the ticket agent could be notified instantly. Booking simply took one more command, updating the availability and, if desired, could be followed by printing out a ticket.
This, however, is followed by . So take it for what it’s worth.
Although you describe it as “the world’s first large-scale computing system,” it was based on SAGE, which the US Air Force used to dispatch interceptors.