How did people synchronize time before modern technologies?

There were no accurate universal time until quite recently and everybody had to figure out how they set their clocks. Many people considered clock towers or the timing of church bells ringing to tell the "real time" and set their clocks based on that time.

Of course, this wasn't very accurate but it didn't have to be. There was no reason to synchronize time accurately across long distances and it didn't really make a difference if your friend's clock was set 5 minutes ahead of yours.

This served adequately until the introduction of rail travel in Britain, which made it possible to travel fast enough over long distances to require continuous re-setting of timepieces as a train progressed in its daily run through several towns.

When the telegraph was invented in the mid 1800s, it now became possible to synchronize clocks across large distances by broadcasting the time over the telegraph. Greenwich Mean Time was developed and all clocks in Britain were set to this time baded on telegraph time broadcasts regardless of local solar noon.

Standard time was originally proposed by Scottish-Canadian Sir Sandford Fleming at a meeting of the Canadian Institute in Toronto on 8 February 1879. He suggested that 24 standard time zones could be used locally, but they were subordinate to his single world time, which he called Cosmic Time. This eventually became UTC time and time zones.

Later in the 1900s, we developed radio broadcast clock transmissions and finally in the 1980s, we developed NTP (network time protocol) which allowed computers to synchronize their times over the internet.