You get a big block of ice, or, in this case, an ice sculpture. You drill a hole in it -- the really good people can somehow drill twisty tubes through it. You pour liquor in the top, and it goes through the tube in the ice and comes out ice cold.

This one, at least, had a little hose with a tap on the other end of the tube -- it's more common that you just put your mouth on the end of the hole.