Most tofu is not fermented at all, as fermentation involves bacteria or fungi.
Tofu is curdled by adding salts to it (not table salt)- usually by adding calcium or magnesium salt (minerals obtained from sea water or natural deposits).
The three most common:
Magnesium Chloride (bittern, or nigari- it's sea water minus the sodium chloride) There are some other, newer things that can be used too.
Tofu skins, or sheets, are made by pressing tofu so much it becomes thin and firm, almost elastic like pasta. It can be cut into strips and used in place of noodles (almost pure protein-good for low-carb diets).
There are also a number of kinds of freeze-dried and spongy tofu textures that are made by different processes. Tofu ranges in texture so dramatically- from crunchy chip-like and springy/spongy prepared to pasta-like or tortilla-like (used for wrapping eggrolls/springrolls) to a firm chicken-like texture, to silky soft to down right indescribable.
Only the ones in this article (silken and firmer) you'll find at most grocery stores. You'll have better luck at Asian markets for the others.