I used 3M headliner adhesive. There are several available, I can see what I used on my 93 as it worked pretty well. It was really coming down above the doors and I was able to spray it in the middle then work my way out to the edges.
The original headliners have some type of foam and its the foam that's disintegrating. I took mine out and bought similar headliner material from a fabric store and simply replaced it. Used spay adhesive as suggested by Rhino.....
Check out the FAQ/Knowledge base thread in the 1st Gen Ram section at dieseltruckresource.com There is a write up in there on how to do it along with a whole barge load of other info on the 1st Gen trucks.