Dashi is the stock used for miso soup. You need just two ingredients: kombu (dried sea kelp) and katsuobushi (dried, fermented, and smoked skipjack tuna ).
Soak the kombu for a couple of hours, make some incisions to release the flavor. Add kombu to one liter of water in a pot. Bring to a boil and take out the kombu just before the water starts to boil (don't boil the kombu!). Add 10 gram katsuobushi (also called bonito flakes) to the stock, bring to a boil and simmer for 3 minutes. Drain stock through a cheesecloth. It takes about 15 minutes to make dashi.
Ingredients miso soup:
1 full tablespoon miso paste (you can use shiro-miso or aka-miso)
Silken tofu, in small cubes
Optional: 1 tablespoon shin mirin (Japanese cooking wine, use the type with less than 1% alcohol)
Miso paste should never be boiled. Put a tablespoon of miso paste in a bowl. In the meantime bring the dashi stock to a boil.
Add a little hot dashi and mix.
Add more dashi, silken tofu, spring onion, wakame and mirin. Wait 5 minutes until the wakame is fully reconstituted. You can soak the wakame beforehand if you wish. That way you'll wash away any 'dust' from the wakame.
This is a basic miso-shiru (literally: miso broth). Many variations are possible.