I used to have an 89 Lincoln Continental - same chassis as your dad's Sable. During the time I had it, I installed a set of 5-1/4" component speakers in the doors, a pair of 3-1/2"s in the dash, and some 6x9s in the back. I cut the plug to the factory amp and wired in standard RCA plugs so I could use an aftermarket amp with the factory preamp wiring to power the speakers (I ran my own speaker wires from the amp though), and installed an additional amp to run subwoofers. Although mine had the premium sound / JVC components in it, so it was set up differently than yours. I would be very surprised if yours had a factory amp.
The stereo in mine sounded INCREDIBLE once was done with it, although i went through a number of alternators. 😱 And the trunk rattled.
It's been a while (8 - 9 years??) since I've had that car, but IIRC, once you unscrew the armrest (don't remember how many screws, 2 I think), the rest of the door panel will be fastened on with plastic clips - get a trim panel remover and carefully pull these out, then lift up on the door panel and it should come right off. Don't forget to unscrew the little chrome door lock indicators that pop up when the doors are unlocked. I just let the door panels hang there while I took out the old speakers and put in the new ones. Factory speaker plug harnesses are not required, but necessary if you don't want to cut your wiring. Make sure to match the speaker polarity when you put the wires in. If you wire it up backwards, it'll sound terrible and it's not fun going back in just to switch the wires.
The rear deck was really easy, just pull off the factory grilles and undo the 4 screws. The speakers were accessible from inside the trunk. Although, I think it required a bottom-mount speaker - some speakers won't mount properly unless they are sitting on top of the mounting surface, and if I remember right, the factory ones are designed to sit below it.
My car didn't originally have dash speakers, but there were grilles, holes, and plugs there for them - so I got some and put them in there. Helped a lot with the high notes, but those little speakers like to blow up if you crank them loud. Bass blockers are a must for these if you add them.