Telegrams had an address header, which also might contain delivery instruction codes. (wait for reply, reply prepaid, etc) The header would also contain word counts, etc.
Larger citys had telegraph offices with many operators. These served as hubs, much as air travel is organized. One operator would cover each “spoke” line. Between major citys there might be several parallell lines, with an operator on each. Major events, political conventions for example, might have a bank of telegraph operators on hand so reporters could transmit thier storys to thier papers.
When the telegram reached one of these offices, the station chief would decide how to route it to it’s destination. This was done using a series of abbreviations for the intermediate stations, again, just as airports have thier abbreviations for routing luggage. I have no cite, but it is not unlikely that many such abbreviations are carry overs.
Each line was a continuous loop. Each key was series connected, so all the keys had to be closed to allow current to flow. Telegraph keys incorporated a switch which was kept closed unless the operator was sending. Only in point-point lines was the sounder directly driven. In most cases, the line drove a relay, which in turn drove the local sounder.
As another respondant mentioned, a single line could serve many stations.
The sending operator would open the line. If it was a low traffic line, he might next send a large number of dots to get the attention of operators along the line.
The sending operator would then “call” the station he wanted. The other operator would then acknowlage, and the message would be passed.
The recieving operator would remove his own call from the routing list before sending the message on to the next station in line.
People tend to think of morse code as slow. Skilled operators could handle at least 35 wpm, which is about as fast as anyone can write, thus for messages that must be written or typed verbatum, it is about as fast as is usable.