Wipe away any dirt from the kombu with a paper towel, being careful not to rub off the white powdery deposits on the seaweed. Place the kombu and water in a saucepan, and allow it to soak for at least 30 minutes.
After soaking, bring the water containing the kombu to a boil. As soon as the water begins to boil, remove the kombu to prevent the broth from becoming bitter.
Stir the bonito flakes or dried fish into the kombu-flavored water, boil for 10 minutes, and take the pan off the heat. Allow the water to cool. When the bonito flakes have settled to the bottom, strain the dashi.

This is a concentrated broth that you can use to taste. I usually mix 1 part broth to 2 parts water and add additional seasonings to make a soup base for udon. You can also use this to add flavour to dashimaki tamago (Japanese omelette) and other dishes.
Dashi can be frozen in cubes.