How do you change the radio panel in a 1980 Oldsmobile Cutlass Supreme?

Yes, they are hidden spring fasteners. It can be quite difficult getting them to release. There may possibly be a proper tool for it, but I've taken lots of them off and never used one. A combination of pulling, prying and steady pressure will usually do it. When they release, they do so all of a sudden so you need to plan for that so you don't break the panel when it lets go. Having said that, the panel, fasteners, etc. are surprisingly strong and while it feels like everything is about to break it rarely does. To replace it fit the snaps back into the holes they came out of and give it a firm thump with the heel of your hand.