I've done a couple of these, as I used to own an '85 myself. It's a little more effort than an ordinary deck install, but things can go smoothly and without headaches if you set aside enough time to do it.
You may be able to keep the factory amp, but I've never had good results doing so---a new afermarket radio has more power anyway. Here's the simplest and most straightforward way I've found to bypass the amp.
Below the right rear speaker, is the factory amplifier. Unfasten both of its plugs FIRST, before you begin doing other wiring.
If the harness you bought at Circuit City fits the plugs behind the dash, use it for your power and ground connections. At the same time, attach four long lengths of speaker wire to your new radio's speaker outputs.
Wiring the front speakers: The dashboard and door speakers run in parallel---you don't need to go into the doors. Remove the top dash pad. There are four screws in the defroster vents, a handful along the bottom edge, and one on each side that you can see when the door is open. Slide the pad backward to remove it, then unscrew the speakers. You'll notice that the speaker's plug has a clip on one side----the side with the clip is the negative wire. Strip some insulation from the factory wiring, and attach your new speaker wire here, with solder if possible. DON'T cut up the factory wiring---just strip and attach---you'll see why later on.
Wiring the rear speakers: Run the wires directly to the rear speakers, and again, strip and splice into the wiring. Some tips for running the wire: The rear seat bottom cushion comes out by pushing it hard backward with your knee, then lifting. Then grasp the bottom of the seatback and pry it out a bit, allowing you to feed the wire upward behind it. Go in the trunk, make an X in the rubber insulation with a knife, and reach through and down to find the wire.
At this point, the amp is disconnected, the aftermarket radio has power, and all six speakers get music. And the cool part is, it's all easily reversible come resale time----this is why I told you not to cut up the factory speaker wiring. Here's how to revert to factory: Cut the speaker wires from the aftermarket radio, tape them off, and leave them in place. Plug the amp back in. Reinstall the factory radio, and that's it.
Aftermarket radio mounting tips: There is a kit for these cars, it sucks, and it's hard to work with. Instead, get a nice file, and use it to enlarge the factory opening until the aftermarket radio fits. You'll also notice that the plastic radio panel isn't very rigid. Get yourself some of that foam that goes under house carpeting. Install the aftermarket radio fully into the plastic dash piece, then attach several layers of foam to the bottom of the radio-----when you put it in the car, the foam will sit down on the metal "shelf" under the radio, providing good support.