Stuff for the job:
- Scott's Shop Towels
For the lightly fogged spots, you just squirt a little of the "Cleaning Solution" onto one of the pads, scrub it on for a while. Keep scrubbing until it looks like it's starting to dry, then wipe it off with a towel. I tried to use about a quarter sized squirt of the cleaner on the pad, and would apply to roughly 1/4 to 1/3 of the headlight.
For moderate/heavy fogging spots, multiple scrubs/wipes will be needed, and you may not see a lot of clarity develop yet. After a 2-3 runs on the bad spots with the "Cleaning Solution", squirt some of the Plast-X on a towel and rub it on there. Again, about nickle-to-quarter size squirts, and about 1/4 to 1/3 of the headlight at a time, and this stuff you can wipe off the excess with a dry towel or rub on until it completely dries.
After the Plast-X, you should start to see some improvement in the lightly fogged areas, and most of the yellow lift off the headlight. If an area is still yellow/particularly foggy, hit it again with abrasive pad, wipe it clean, and then hit it with the Plast-X until you're happy.
Don't worry about scratches. This process will help reduce most of them, but isn't going to completely eliminate all of them. The point of this process isn't to remove every slight imperfection out of your headlights, it's just meant to clean'em up so for optimal lighting performance. If getting out ever little scratch is what you're goin' for, there are other kits out there for that.
After a bunch of passes with the cleaner and Plast-X, it may be just a wee bit fuzzy in the worst spots, but the rest of the headlight is clear. Now it's time to apply the Headlight Coating. I don't know what it is about this stuff, but it makes the headlight WAY clearer than just the cleaners/Plast-X alone. On top of that, it acts as a sealer to protect your headlight. Just spray on a coat, wait about 3-5 min, spray on another coat, and you're done. Then you should be able to get by with just cleaning the headlight once a year with Windex (or Invisible Glass), and hitting it with the coating again, and you shouldn't have to worry about the headlights degrading ever again (at least, according to Scotty Kilmer, who has a Youtube video about using Plast-X + the Headlight Coating. I tried following the instructions in his video, and didn't think the Plast-X was getting the job done by itself, and decided to go get the Two-Step kit to help).
So there you go. Here's a comparison picture I took of Azumi, after treating the driver-side headlight on her with the process (ignore the black dot on the hood. While I was cleaning the throttle body on her, some how I punctured the lens on my phone's camera, and put a pin-hole scratch on the camera itself). With a little elbow grease, your Kizashi can also have clear headlights like it just rolled off the assembly line.