First off, many thanks to Alissa for guiding me through this (several times).
Dashi is a traditional stock, used widely in Japanese cooking. There are several variations, most of which make use of "konbu" - dried kelp seaweed. Konbu contains glutamic acid, which gives the broth umami (savory taste, the fifth basic flavor along with bitter, sour, salty, and sweet, sensed by human tongues). The other ingredient is usually either "katsuobushi"- dried fish flakes - or "niboshi" - dried anchovies. This variation, konbu and niboshi dashi, uses kelp with dried anchovies.
Start off by making slits in the konbu, then soak it for several hours (if possible) in the broth-water-to-be. I think 1 large piece is a good amount for 1.5 to 2 litres. Behead and gut the niboshi. I think 1.5 oz is good for up to 2 litres, but I could be wrong... I haven't found or heard of specific numbers, so I'll have to play around with it a bit and see what works.
Add the niboshi to the konbu water, then slowly bring to a boil. As soon as it boils, drop in a dash of cold water to halt the boil so that you can remove the konbu. This part sounded weird and ritualistic to me, but then I read, in 'On Food and Cooking,' that konbu contains iodine that is only released if it is boiled. Bring it back to a boil and cook for another 1 to 2 minutes. Strain the broth through a fine strainer, then it's done.
Now I have to venture into some Japanese cooking...