This was another chant that started up in the early '70's. It would be sung when, for example, Dundee were 3-0 up and winning the game very easily. A chorus of "Show them the way to go home..." would ring out to embarrass the opposition. The tune is a really old composition going way back to the 1920's called "Show me the way to go home", and is mostly known as a drinking song.
Below is a wee karaoke to get a bit of practise!