Basically, the only thing you keep from the old radio is the knobs for the climate controls, besides the wiring harnesses.
You're going to go to Autozone and get a Ford Factory Radio Removal Tool, which looks like a 'U' with prongs on the end. You're going to push both into the two holes on the sides of the stock unit. Push to the outward sides of the unit, and pull out. You're then going to unplug all the wiring harnesses, and pull off the climate control knobs. You're obviously going to need to get a dash install kit, which you can get here: American International kit
or here: Metra kit
. Personally, I have the Metra kit, because I've had my car for two years and I think that was the only one available then. I think the American International kit looks better though, although I've never used it.
Anyways...after you get the dash kit, you're going to need to mount the stereo just as you would any other stereo, except in the dash kit. You're then going to have to run the wiring harness that is included down through the dash and the kick panels, then through the channels that run below the door, through the seat, and plug it into the appropriate plugs at the rear of the car, where the factory amp/control unit is located. There will be a harness for the speakers, which will be 8 wires in all, and an extension for the antenna.
After you've connected the harnesses at the rear of the car, connect ALL the harnesses to the dash kit and the new stereo. Check to make sure that everything works, including the stereo, all HVAC controls, and rear-defroster. Once you've been successful in getting everything to work correctly, you need to install the stereo. This may be a pain, I know it was for me. There are a crapload of wires and such that you need to make sure fit in beneath the stereo. Get them all situated, push the stereo in. If it doesn't fit, you'll need to use a dremel or somethign to trim the edges. Thats all you need to do to install an aftermarket stereo in a 96-99 Taurus/Sable.
Oh yeah...depending on the stereo you use, you should upgrade the factory fuse in teh passenger compartment fusepanel. I think that the stock fuse is like 3.5 amps or so. I have a really nice stereo, so I had to upgrade the fuse to a 6 amp (or so) fuse. Don't go any higher than 7 amps, or you run the risk of burning up your wiring. All in all, the install should take you about two hours or so (depending on the fit of the dash kit). I'll post a picture of my stereo in the car later tonight.