How exactly do 1950's rotary phones receive phone calls?
The way standard corded landline phones work hasn't changed much. That is why you can often still use old phones on a modern phone line.

When a phone line is idle there is about 50V DC between the two wires. When it rings the exchange superimposed a low frequency AC ringing voltage (about 100V iirc) on the DC. The ringer in the phone is connected to the line via a capacitor so it isn't affected by the constant DC but is caused to ring by the AC. In phones from the 50s the ringer is an electromechanical bell.

When someone picks up the phone the main phone components are connected to the phone line and presents a DC load (phones typically used carbon granule microphones which required DC power). The exchange detects this load (IIRC in the old days this was done by connecting relay coils in series with the supply to the phone line). If the phone was ringing the exchange exchange stops the ringing and connects the call. If the phone was not ringing the exchange presents a dialtone and waits for the user to dial. An analog circuit known as a "hybrid" seperates incoming and outgoing audio. In nearly all phones the hybrid circuit is crude and leaky which is why you can hear yourself in the earpeice.

The only thing that has really changed about the interface phones use is the method of dialling. Old phones pulsed the DC load they place on the phone line on and off. Modern phones send DTMF tones. For many years phone exchanges accepted both but I believe support for pulse dialing is now being phased out by some providers.