Funny thing is I'm not going as "by the book" as I'm supposed to. I don't have a clay bar so I didn't use one, I just washed and dried the car, then wiped it down with a microfiber towel.
I'm using a random orbital buffer I got several years ago from the parts store. It doesn't have any of those fancy pads like Porter Cables and more expensive buffers have, just microfiber cloth pads. Like one of these
I have 3 pads, an hand applicator pad, and a bunch of microfiber towels.
After I wipe the surface off I put a pad on the bugger, put some rubbing compound (these are the ones I used)
Put some on the pad, then spread it across the working area (2x2 or so), then turn on the buffer and go over slowly, steadily, and evenly. I long back and forth strokes.
After the compound is worked in I wipe it off with a clean towel (it says not to let it dry so I don't). Since the Prizm's paint was in such poor shape, I repeated this process 2-3 times depending on how bad the area was. On the final time I wiped it down a second time with a new cloth, making sure to get all of the residue off.
This step gets off the many of the scratches, haze, and oxidation. Once you're done the surface will look much smoother though it'll be a bit dull. That gets remedied with the next step.
After this I switched pads for use with the polish.
I repeated the steps as I did for applying and removing the rubbing compound.
This step give the paint its deep luster and shine. It makes the paint feel super smooth to the touch..love that feeling.
For the final step I used this:
This is the stuff that protects the finish.
I used a hand applicator (just like these)
and applied the wax to the the applicator, then spread it in a circular motions across the working areas, applying more as needed. Then I let it dry.
The last step was to use a clean buffer pad and remove the wax from the surface, going over multiple times with very light pressure, just letting the buffer glide over the surface.
And that's it! That's the process I've been using, and the results speak for themselves.