There was only one method of voice encryption early on, and that was the A-3 system, but it was old and some top commanders correctly assumed that Germany was intercepting and cracking those conversations.

From 1943 those top phone conversations were encrypted by SIGSALY, developed by Bell Labs (with contributions by Alan Turing) for the US Army. I don't pretend to know how the numbers work - Here's the patent if you have a head for such things - but essentially it took 25 samples per second of the voice, and encrypted it using the white noise from two duplicate records, playing in absolute sync on either end of the call. Only two of the same record were ever made, and they were destroyed after each use.

It was a clever but very expensive bit of kit, with each terminal spread over 40 racks of equipment weighing 55 tons. As such it was only installed in nine locations during the war plus a small ship that followed MacArthur around the Pacific, and used for only the highest levels of communication, being used for 3000 conferences during the war. The White House didn't have its own terminal, but rather had an extension line to the Pentagon's terminal, while Downing Street ran the equipment from the basement of Selfridge's.

It was the first device to digitally quantize speech and to transmit speech by PCM. So it wasn't analogue audio communication, but rather digital audio on analogue hardware.

The NSA has an essay that explains the technical detail... well, at all, while the International Churchill Society has an article that discusses some of the British side.