Intriguingly, dashi is appearing in the cuisine of some established Western chefs, including Eric Ripert (Le Bernardin) and Jonathan Benno (Per Se). Check out the New York Times story about this trend.
Making dashi is easy, but it requires a trip to an Asian market for the two key ingredients: kombu, an edible type of kelp cultivated in Japan, and katsuobushi, fine shavings of dried bonito, a type of tuna.
The process is simple: Place a 4- to 5-inch strip of kombu in a pot with about 5 cups of cold water and slowly bring the water to a boil. Just before the water boils, remove the kelp and turn off the heat. Add a handful (2 or 3 Tablespoons) of bonito flakes and steep. When the flakes sink to the bottom of the pot, strain the liquid through a fine sieve. What's left is a very delicate, clear broth that smells faintly of the sea.
So far I've used dashi as a base for miso soup, for udon, and as an ingredient in dishes such as braised gobo (burdock) with carrots, a traditional Japanese New Year's food. It appears in most of the recipes I've been eyeing in various Japanese cookbooks.
Check out the video below the jump for a decent demo of making dashi. Note that it appears to use different proportions and an extra step (adding cold water before putting in the bonito flakes) from my simpler, handed-down recipe (which, by the way, is untested by our Test Kitchens). You can also try our vegegarian dashi recipe for a fishless alternative.