The wax needs to be applied to the chain and specifically its rollers/pins. Nothing else needs waxing on your bike. (ball bearings need grease or oil, not wax)
The reapplication process is to remove chain from bike, and degrease it with a can of degreaser. I use two rinses, first gets very dirty and the second less so. Then the chain is hung to dry.
I use an old electric frypan to melt my wax. I lay the chain in it back-and-forth so there are no overlaps. Then melt the wax, using an IR gauge to read its temp. Around 150 degrees C is good IMO, where the wax is liquid but not super-dangerous. It should be clear too and have lost all the white.
With the chain submersed in the liquid wax, I look to see the streams of bubbles coming off the chain. This indicates something is cooking off. Once those bubble streams drop off, power down the pan and let it start to harden. You want to get the chain out without the wet wax running out of the roller, but you don't want the wax to be too hard on the outside.
Let the chain cool so you can handle it. The wax on the outside will flake off easily, making a bit of a mess so do this somewhere you can sweep.
While the chain is cooling, clean your chainrings, jockey wheels, and cassette. Use gear floss or something to get in between cogs and make it shiny and pretty. Also clean road grime from your frame and from within the derailleur cages.
Once its all cool, refit the chain, and test ride. No additional lube is needed, though you might choose to oil or grease jockey wheels while the chain is off.
Some boilers have a "low spot" where contaminants collect. Or you could peel the hardened wax from your pot and simply cut off the bottom centimetre or so, whatever thickness looks extra dirty. Then dispose of that bit properly (area dependent)
Another option is to melt the wax so the dirt sinks, and decant the top clean layers to a temporary vessel. Then tip the bottom layer into a scrap container, scrape the pan out, and throw the wax when it has set.
The cool thing about wax is that it melts back together so easily, and its relatively cheap, so that I could throw the whole pot full out without qualms.
5 kg of paraffin wax cost me around $35NZ, and I used less than 800g in a cooker and after two chain cleans its barely dirty at all.