Okay just finished and I stopped to get coffee and put things away and wash out my rags... probably a lazy half hour total?
Before is 2004 original headlight, not cleaned or even gone through a car wash in a few years? Oops. Garaged NOW, but for like 13 years - parked in open parking lot in Gulf Coast of TX so OMGZ all the sun/UV in the universe...
After is using Ajax (with bleach which is all I had, so made sure to wear clothing that was okay with bleach spots if I got it on me). I started to use Barkeepers but it's really fine and didn't feel as abrasive as I like and I'm running REALLY low on it, so I got out the other stuff. Honestly, look for abrasive cleansing powder/stuff you'd feel comfortable using on your bathtub and its likely safe. Or just use barkeepers since it is a polisher as well as having better abrasives=more powerful than toothpaste.
Otherwise: several rags, water dish, UV protectant (I have armorall UV spray), then turtlewax if you want a bit more lasting coating but don't feel like doing the UV coating in a can right now.
1. Wet/ring out rag ONE (do not use this after scrubbing part). Add powder/cleaner to the RAG, start making circles on light surface, scrub, reload with a bit of powder until you feel it's getting gritty but still damp enough to get on there. Scrub a few minutes over the whole light surface. Use a rinse rag or lightly spray with water to check progress. Mine took about 5 minutes on each side.
2. RINSE, wipe down and let it dry or use dry rag to wipe down well.
3. Lightly coat/spray with your UV protectant. I used the Armorall I have for rubber/plastic surfaces. Sprayed, let it run down used a the slightly damp drying rag to lightly wipe so the surface spray was evenly distributed. Let it dry a minute or two (do the other side and then go back to the first one). Repeat if you're feeling generous. I usually do 2 coats.
4. Allow drying, then use paste wax as optional final step. I used a lightly dampened clean rag, did the dab/swirl on the lights, waited for it to haze (hot today so took just a few minutes), then buff off. AFTER pic is the finished results.
I include a split screen comparison shot so you can see the difference. Again, took me MAYBE 30 minutes start to finish and I have all the stuff on hand. The lights are going on 17 years old at this point so I don't have a problem with them looking like this - not crystal clear, but they'll do for the driving we do with this vehicle. If I was doing LOTS and LOTS of driving at night, I might spring for the spray coating and do it up using a drill bit polisher and the fancy coating, but I do this version, it lasts months if not longer and I can pop out there and do it pretty fast if it starts hazing up bad in 6 months or a year...