How did car telephones work, in pre-cellular days?

radio telephones.

Yup, radio telephones. Frank Cannon on the Cannon TV series in the early 1970’s used a mobile phone that he would call the operator to complete his call.

Not very well. They were incredibly expensive, both to use and to buy and have installed.

Audio was medium to poor and coverage was minimal compared to today,

I’m a child of the 50s, and I recall when “car telephones” became a consumer item in the 80s or thereabouts. As the others have already explained the technology I won’t go into that, but the packaging was like a small suitcase with a corded phone hanging from that.

Prior to that the technology for full duplex radio telephone did not exist, as far as I know – or anyway, not available for off-the-shelf consumer purchase. The only tech available then was “actual radio”, whether on police bands or CB (citizens’ band). And that wasn’t full duplex (meaning that you could both talk and ‘listen’ at the same time, sort of the way that some folks do all the time).

A radio signal would be sent to a receiver station where a telephone operator would direct the call via land line to it’s destination. If the call was to be received by another radio phone, another operator would direct it through a radio transmitter to the final destination.

I had one. I was a ham radio operator and had a 2 meter radio in the car. I would connect to the repeater and then punch in a code for the autopatch. The dial tone would come up and I’d make my call. Only drawback is anybody on that frequency could listen to the call.

Also, it was the size of a medium sized purse.

^^ you can still do that and I have at times when backpacking out of cellular range but still in range of several repeaters with autopatches.

@ARE_you_kidding_me Yes. I let my license lapse 35 years ago but I know of people who still do it.

Analogue is basically radio. And calls can be eavesdropped on through police scanners.

A car phone was a pricey luxury, and a bit of a status symbol, back in the 1980s. Having one seemed to scream, “I’m a very important person!” or “I’m really well-off financially.” I never had a car phone, and neither did Mr. Love_my_doggie. But, a very arrogant, self-important relative of ours had car phones throughout the decade.

Wikepedia has a good, detailed history and tech of car phones which can fill in any gaps not covered above.
They weren’t very practical, as others have alteady said.
The introduction of cell phones pretty much caused the extinction of the car phone.