Very easy, but time consuming to really do it right. Well worth the effort, though, and a very enjoyable result.
Your headlights may look like mine did, below, if they've never been refinished or replaced on your old Contique, or any car for that matter:
Buy any headlight refinishing kit from any auto store, or... you can go to Lowe's or Home Depot (or any hardware store) and get your own set of sandpapers and polishing compound.
I'd start with 600 grit wet sandpaper, for really bad headlights like mine. Even so, it will take quite a while of sanding to get a good result... I sanded for about 30+ minutes with hard pressure, very carefully to ensure even and thorough sanding.
It works best to just take off your headlights, so you can hold them at an easy angle or set them on a table (PUT A DROPCLOTH OR CARDBOARD DOWN!!! They will scratch your table up, and piss off the wifey).
Start at one end of the headlight, and sand in 1 direction only, ie - back and forth horizontally. Work your way all the way across the headlight in a "row", then move up a little bit, and work your way back, always sanding in 1 direction. Keep rinsing and re-wetting your sandpaper and the headlight, either with a little tray of water next to you or with a mister/spray bottle. I used a tray. Keep going like this.
Next, use 1000 grit. Start in the same spot. Sand in the other direction, 90-degrees different, ie - up-down direction now. Again, work your way carefully across the headlight one "row" at a time and don't miss any spots. Sand ONLY in that same direction - ie - up down. Keep your sandpaper wet and rinsed at all times.
Next, 1500 grit. Start in the same spot. Switch back to horizontal sanding.
Next 2000 grit, same spot to start, up-down sanding.
Next 2500 grit, same spot start, horizontals sanding.
Finally (whew, tired? Yes, I bet, but this may be the hardest part)... use the polishing compound either included with the kit or separately bought. If you buy it separate, best to look for headlight or plastic polish. It looks like wax, but thinner & runnier. Rub the polishing compound in using 100% cotton rag or some soft polishing cloth (included in the kit, usually). Rub, rub, rub, RUB, RUB!! Rub hard! It may start drying on you, and that's ok. Rub away with firm pressure until you can see them shiny and clear again. You'll love the labor of your hours of hard work: