The tone pot has two connections and is being used as a variable resistor (unlike the volume pot which is wired as a potential divider and has three connections). The tone circuit is the variable resistor and capacitor in series between the output signal and ground. You can have the capacitor and resistor either way round, it works just the same.

The capacitor will pass the high and most of the middle frequencies but will stop passing the bass frequencies depending on its value. The bigger the value, the lower down the frequency range the signals start to get blocked. So with the tone pot on 0, there is no resistance between the capacitor and the pickup signal, so most of the upper frequencies get grounded, leaving only the bass frequencies being passed on to the amp, and hence the dull sound. With the tone pot on 10, you have the full resistance of the pot reducing the signal level going to the capacitor, so almost all of the pickup's output is sent to the amp.

0.022uF is the 'standard' modern capacitor value for humbuckers, as these are normally darker sounding than single coils, which will generally have 0.047uF capacitors, so that when rolled off, both types of pickups still have enough low-mid frequencies left to make the notes sound bassy but still distinguishable. But what you like your tone control to do is very subjective, and not everyone likes the dull tone that full tone roll-off can give. If you are never going to use it backed off that far, why have it set up for that, and why not have a less aggressive tone control arrangement? So I now generally fit 0.015uF capacitors. Which still gives allows quite a dull tone, just not that dull. But it is a personal preference, so really you should try some different values and make your own mind up what works for you with a certain pickup type.

Gibson have used 0.1uF, 0.047uf, 0.033uF and 0.022uF caps on humbuckers for their tone pots in the past. 0.022uF has been their cap selection for many years now. But remember that Gibson came from a jazz guitar background, and the Les Paul was originally designed to be a jazz guitar, so Gibson needed it to be able to get very dark and mellow sounding, hence the larger value caps on the earlier guitars.

Note that the tone capacitor value will make zero audible difference with the tone control set to 10. There is some very minor treble roll off with bigger value caps, but you'd need a spectrum analyser to detect it as it's in the order of a 1/8dB level difference between 0.047uf and 0.022uf at the higher frequencies. You'll probably roll off more treble by having a guitar lead that's a few feet longer than your standard length.