Dashi is a stock made from kombu (kelp) and katsuo-bushi (the dried fish known as "bonito"). Along with shoyu (soy sauce), dashi is used most frequently in Japanese cooking in everything from soups to simmered vegetable dishes. Dashi is the foundation for countless dishes. But it's not vegetarian. Here are two recipes: one for real dashi and one for daishi (vegetarian dashi).
Place two quarts of cold water in a large deep pot. Take about 20 inches of kombu/kelp (about 1 1/2 oz.), and carefully and thoroughly wipe the kombu with a clean moistened cloth (do not wash kombu as it removes the flavor). (Or just pop it in the pot. The white powder is msg.) Place the kombu into the pot and slowly bring the water to just before the boiling point, regulate the heat so that the water never actually boils. By simmering the kombu in this way you are releasing its flavour. Once the kelp is tender (about fifteen minutes), remove the seaweed.
Add 3 cups of loose bonito flakes and turn off the heat. Once the flakes have sunk to the bottom of the pot (about a minute or two), strain the stock into another pot or receptacle using a colander filled with cheesecloth or a large coffee filter. The finished dashi should be a light golden color and free of any bonito flake particles. You can store dashi in the refrigerator for up to three days but it's best to use as soon as it's made.
For a vegetarian version, do the same thing with the kombu but then flavour the stock with a splash of mirin and less than splash (perhaps half a teaspoon) of rice vinegar.
You can also purchase powdered dashi and bing into some water. Many of the Japanese restaurants I've been to do this. I don't go back. But since I'm not eating at your house, hey, go ahead.