Why you do it
Pressed Tofu is a sturdy form of Tofu used in situations where normal tofu would fall apart and disintegrate, such as in salads or in stir-fried dishes. Commercial tofu already comes in different levels of firmness and manufacturers control hardness by varying the amount of water they press out of the tofu. What you are simply doing is squeezing even more of the water out of your tofu to increase its firmness even more. The trick is how you squeeze the tofu without making it crumble from the pressure.
Pressed tofu is actually quite common in East Asia outside of Japan. In Southeast Asia it is called Tau Kwa. There is even a style of Haka food called Yong Tau Foo where minced fish is stuffed into Tofu. Obviously if the tofu is not firmed up beforehand, there would be no way to stuff anything into it. Often the pressed tofu is deep fried. The Teochew stew this type of pressed Tofu in soya sauce with goose. Fried pressed Tofu is also an essential ingredient in Pad Thai, a common type of fried noodles from Thailand found worldwide. It is also used in a dish called Mee Siam, which is a ‘Thai’ style vermicelli dish popular in Singapore and Malaysia (but paradoxically not in Thailand/Siam).
How you do it
Place a block of tofu onto a flat bottomed tray or dish after draining away the water it comes in. I usually use the tray from my toaster oven. It should be of the firm type, sometimes labelled as ‘stone’ tofu. In any case, be very careful not to damage the tofu in anyway as any localized weakness in structural integrity will cause the tofu to crack when it is pressed.
Wrap some cling film tightly around the side of the tofu, twice. Don’t wrap the bottom because that’s where the water escapes from and cut away most of the extra cling film protruding at the top. You are only interested in constraining or reinforcing the side walls so the tofu doesn’t bulge sideways and burst. Some people use towels but I find that cling film is the best way of preventing the tofu block from crumbling under pressure.
Place a stiff cutting board over the tofu, making sure the tofu is exactly at its centre. Place a can of food on the cutting board to start off with and gradually increase this to 6 cans over the course of an hour. When you notice the cutting board tilting to any particular side, adjust the position of the cans to bring it level again. Wait another hour after you reach six cans and you are done. Your tofu should be sitting in a pool of water about half as high as it was when you started, and twice as firm.
One example of a recipe that uses pressed Tofu is my Chinese Pork Curry recipe.