I have to tell you there are still a few airline city ticket offices left in London. Only recently did Iran Air close up in Piccadilly (the aircraft models are still in the window), and just next door Aeroflot carries on.
http://maps.google.com/?ll=51.507424...325.31,,0,2.54
Korean is still around as well, and there must be some more.
Now, to the main question. Within an area with good telephone communications, like the US example given above, there could be a central office (they often had several regional ones) that agents could telephone, where there were some real examples of business systems ingenuity from the pre-computer days, with vast card index systems managed by operators who took the calls and filled in reservation cards in special filing units, customised to be within arms reach.
The USA had toll-free numbers at an early stage, but they were not common elsewhere so it was preferable to use Telex, getting a response maybe an hour later. It was more straightforward then; fares were known, being read from printed manuals issued for the season, and few flights filled up well in advance.
For bookings on airlines from overseas, a concept called "Freesale" was used, which basically said any agent could sell a ticket and then just advise it by Telex retrospectively. There would be an overnight confirmation, or occasionally a denial if it was full, but this was sufficiently infrequent in days of sub-50% average loads that it was an acceptable way to work.
For international airlines they would generally divide up the seats for each flight between different sales offices. Thus BOAC doing London-Sydney with maybe six stops along the way would initially allocate seats in varying proportions depending on their experience to their various offices, so Singapore would get say 20 eastbound seats to sell, maybe even a few to off-line places like New York. Each day this was reassessed for each flight in the light of everyone's bookings, and the numbers went up and down and were Telexed round to everyone. There's a poster over on PPRuNe who used to do these calculations for BOAC's commercial department in the 1960s.
There were no (well, few) computers, but plenty of ingenuity in the office.