The clay bar, if used correctly, is very good for removing almost microscopic dirt. The routine (and you wouldn't want to do this too often as it takes a while) is this:
1. Wash and dry your car thoroughly. No short cuts.
2. Take a smallish piece of the clay bar and using the lubricant spray (VERY IMPORTANT) gently polish the whole car. Bearing in mind that the piece of clay bar you'll use will be about the size of a 50p piece, you'll see this takes a while. You have to frequently refold the clay bar to give a clean side to the paintwork.
3. You could, at this point, use a cleanser for the paintwork such as Zymol HD Cleanse.
4. Applying the wax.... If you're using Carnauba wax, this is not put on by cloth but by hand. Take any rings off, put a 10p coin size in the palm of one hand and rub both hands together vigorously to warm and melt the wax. Then rub in using the palms of your hands! Kind of weird, particularly if anyone is watching!! Depending on which Carnauba you use (there are many grades) you either wipe off immediately or leave for 20 minutes. Generally you'd wipe only once hard in the direction of the lines of the car - it's not polished off in the normal way.
The advantage of the wax is the easy application and non white residue. You can keep applying it, coat after coat too. It should last 3 or 4 months on a daily driver.
All of this will sound terribly anal. Actually it is terribly anal! However having had a few 'serious' cars, I do like to keep them very shiny. The clay bar is kind of fundamental to starting the deep shine.
Not sure you can really capture the depth of shine in a photo: