Probably some screws, and some clips around the perimeter of the panel. Also likely screws running through the armrests and door pulls into the door.
See if you can find a shop manual for your year. You'll use it all the time.
Yeah like some have said for screws around the perimeter, some even add some over the years. When they are all out, lift up on the panel to remove it, to get it out of the grooves on top. The door pulls come off with the door panel and are screwed on backwards.
I couldn't ever find anything in the shop manual concerning door panel removal, but perhaps I missed it. In any event, I found this a while ago, http://1976eldorado.com/door-panel-removal/ . It's for an Eldorado, but I believe that the door panels are pretty similar to the RWD Cadillacs.
Automobile(s): 1968 Coupe Deville, 87 Mustang, 00 Mustang
Re: door panels
There is a place I found that specializes in repairing dash pads. I think they work on door panels and other stuff too. My door panels are damaged as well. They cracked in the middle while otherwise they are not in bad shape except for the gaping holes where it cracked in half.