And how was this information transmitted to the public before clocks were cheap and small enough to own?
There is an answer in a previous question
In a world that can't agree on anything else, how did we all come to use hours, minutes and seconds?
As for transmitting information hourglasses and time candles could be used to keep track of time. On Navy ships the day would be split into 6 4 hour "Watches" during the working part of the day a bell would be rung for every half hour of the watch. 1 bell for the first half hour 8 bells for 4 hours and then begin again. Some towns did something similar ringing a bell or blowing a horn to mark 8:00 12:00 and 4:00.