Just wondering when the modern dispatch system we know from movies and TV began and what the police did before such systems existed.
There were a few different ways:
Many cities had call boxes that called directly to the police station. An officer out on the beat could call in if he needed backup or maybe needed someone transported.
Prior to that, the call box may have just been a bell that rang at the station and alerted someone there as to where to send help. Variations on how the bells were rang told the station what the officer needed.
Some cities used lights in high places. The lights would mean something and they were controlled by the police station. Officers out "walking the beat" would keep an eye on the status of the lights. How the lights were arranged and what they meant varies greatly between places.
Many towns and cities would actually use radio stations to get messages out. For example, all the cars were told to be tuned to the same station and a call for assistance would come out over the radio. Some larger cities even created their own radio stations for this purpose. WNYC is a good example of this. It is now public radio but was originally created to dispatch officers.
The first portable radios were huge, had tubes, and took a while to warm up. They required a lot of power so really were not that portable. Officers would have to go to the car to use them. Early on, only certain cars carried radios. These were radio cars. Actually, being a radio car wasn't a bad gig. Officers could ride instead of walk and were in a climate controlled vehicle.
Prior to all of that, officers really relied on their own knowledge, instinct, and training. Some small localities would have one person out on patrol all by himself. Larger cities would pair up officers and assign them a specific beat. Sometimes they were required to check in so often and if they hadn't, that was when backup was sent. Officers also wore a whistle, which could be loud enough for other officers on nearby beats to hear.
The technology has come a long ways. My state is massive at nearly 100k square miles. We have under 200 state troopers to patrol over 8,500 miles of highway. There are, literally, times when there may be one trooper on duty in an area the size of Connecticut. All of our highway patrol troopers are dispatched from one location in the southeast corner of the state. There isn't another dispatch center anywhere else in the state for highway patrol. Car locations, speed, live dashcam feeds, etc, can all be monitored in real time. The ability is present to even monitor body cameras (when we get them) and to monitor the biometrics of individual troopers (we are not really looking at using this technology any time soon).
Whistles were used early on. They could be heard from a far distance, which would be used to summon help.