Participants sit in two adjoining sound-proof booths and converse using microphones.
As Duane explains it, what the person in the in the first booth says is beamed up to an Earth-orbiting satellite, gets scrambled "so the bad guys can't understand nothing", and bounces back to the person in the second booth "clear as day".
In practice, the satellites pick up extraneous communication causing confused conversation. However, Chief Maxwell Smart does praise the comfy seats.
[GS95 Episode #1: "Pilot".]