The rite of exorcism itself is complicated if you believe in the faith system which supports it. Assuming that one does believe in this system then the following would take place.

In the 1970s as generally now there are steps to go through, generally one contacts a parish priest and then it is escalated up to the bishop of the area. If the mental health checks and medical stuff does not solve the problem then an exorcism can take place.

In the 1970s the mental health stuff would likely have been less strict that it is now. The ritual for exorcism itself has been revised in the 1990s. There would still need to be a bishop consulted in almost all cases though, as exorcists for a time were fairly rare (in that there were not many priests specializing in this field).

You can find the modern prayers and rite on catholic.org.

To read a book about exorcism before the 1990s the best known one is probably Hostage to the Devil by Martin, though he is a) dead and b) was not in good standing with the roman institution towards the end of his life.

The book itself is fairly factual in its descriptions of the rites, prayers and procedure, but the actual events hold more impact if you are a catholic or are inclined to believe in demons/ the devil.