You declare all the assets you own* in your tax declaration (bank accounts, properties, art, cars, equity, ...), even if abroad. You also declare your debts.
I don't know how they enforce/check that, especially for foreign-based assets though.
* except for household and personal common usage goods
OK, cool, but you didn't explain how does that fix wealth inequality in Switzerland or make wealth taxation fair? You just described a tax declaration system, not a taxation system.
Anyone can declare assets anywhere but if they're not taxed, or taxed very little, then inequality grows. So does Switzerland do this better or fairer than other countries?
Because you pay a percentage of your total wealth in annual taxes every year (in addition to your usual income taxes).
It differs between cantons (states, kinda) and has progressive banding. Someone with 100k in wealth will pay maybe 100-200 or so. If you have 100 million CHF, in Geneva you would pay around 1 million per year in taxes on that wealth.
As the OP stated, it is global assets and wealth, so foreign/offshored investments still attract the tax. Plenty of people choose to be resident in Switzerland even with these taxes.
Well, you asked how it worked, not whether it was effective at fighting inequality.
My understanding is that it's not very effective, because any foreign-held asset is pretty much hidden from Switzerland, unless there's an agreement with the country for this kind of information.
* except for household and personal common usage goods