It is important to note that arrangements varied greatly from place to place depending on the date, local conditions and the telephone company that first installed the network.
Party lines were common even in high density cities for many years of telephone service; they saved about 35% of the phone cost which enabled people of modest means to afford a telephone. In the 1950s, party lines were mandatory in some places until the phone company could catch up with heavy demand for new service.
Party lines didn't only share the cost of running a line to the subscriber, but also central office costs as well since it reduced traffic peaks. Central offices had to be expanded before mandatory party service could end.
Indeed, a major motion picture comedy was made about two people fighting over use of a party line they were forced to get.
In some US states party line service is no longer offered at all. In other states it is too existing customers only. I don't know if any state allows new customers to get such service. The savings today are only about 5%.
As mentioned, technical arrangements varies. In cities, it was
2-party service, Bell using arrangements of tip and ring and ground (someone else can explain better) so only the desired party was rung. In later years, each subscriber had their own number and it was transparent to the caller. The independents often used frequency ringing.For very rural service, more than 4 parties would share a line and ringing cadences were required.