The night before, place black beans in a bowl or pot and cover with plenty of fresh water, submerging them by at least a few inches. Let sit overnight.
The next day, drain and rinse the beans.
Put beans in a food processor or blender and pulse a few times to break them up.
Add water to the beans in the blender and puree until a liquid slurry forms.
Strain mixture through a mesh sieve, collecting liquid in a pot. Press beans with the back of a spoon or a spatula and/or mix vigorously in the sieve to ensure as much liquid drains as possible. Bean solids left in the strainer can be composted or reserved for other uses.
Add salt to liquid. Heat liquid over stove, bringing to a gentle boil and stirring constantly to ensure slurry stays nicely mixed and does not burn. After about a minute of cooking, the liquid should become very thick and paste-like.
Pour slurry into a mould, which can be a container or small baking dish.
Let rest for at least an hour. The slurry will cool and solidify into tofu.
Once fully set, remove from mould and use as desired. (See notes below.)