In Ghostbusters and other films of the time, a combination of animatronics, traditional puppetry, sculpture and design were used to create 'creatures'.
The 'creatures' and ghosts in Ghostbusters would be produced in many different versions: a static sculpture, scaled-down version, animatronic version, and some like Slimer and the Library Ghost needed to be worn by a performer.
Full size and scaled-down sculpture models
Animatronic head
“His mouth and eyes were operated by puppeteers dressed in black, sitting below and behind him. Someone else’s arm operated the tongue. The camera was locked off and we would move ‘Slimer’ around according to the shot." VFX supervisor John Bruno
Ghostbusters.net
'Ghostbusters Special Effects: Slimer, Stay Puft & the Library Ghost'.
Quick video showing you how the effects work and just how hands on they are.
American Cinematographer Magazine
'Visual Effects For Ghostbusters'
There is also great interview with Richard Edlund at the bottom of this but I can't link it separately.