ISTR the process is basically

Wash the car with a detergent that will remove all of the old wax and polish, so you're dealing with paint. Just run your finger down the car and feel all the little bumps before you start.

Then you need to deswirl the car, so that as many of the swirl marks, scratches, etc are removed.

The clay bar it all over so you're really dealing with just paint and it is smooth. Now run your finger down the car and try to feel any bumps.

Then you're into waxing and building up the finish.

Once all this has been done, you just need to go over the car with a micro-fibre cloth and some Quick Detailer. And those photos were done after the car had been driven home in the rain, and we went over her, just, with that bottle of detailer and some good cloths.

To be honest there are so many possibilities, specialist knowledge required and tools, that I got a professional to do it. There are so many variations in paint, do to age, condition, etc. That I trusted a pro, but watched him and asked lots of questions. For example, when he took off a little too much paint on one wheel arch it was over to him to fix it.