I must be old fashioned. I hear a song playing on the radio and I visualize the singer recording it over and over, each time adding some more harmony.
No, it is done today with software. The singer sings a song only one time and the software "sings" the harmony in the singer's own voice.
I found links to the software. They explain how it works and how it is made "realistic" and musical.
Of course, today the software also fixes the pitch errors of a singer's voice which is why most singers live cannot sing worth a damn.