1. In a pot, bring the water to a slow boil. Add the wakame; slowly simmer for 20 minutes. (The longer you simmer it, the less sharp its taste.) Add daikon and onion during the last 10 minutes of simmering and carrot during the last 5 minutes of simmering.
2. Take a small strainer and place it just in the soup. Take spoonfuls of miso and mash into the soup through a strainer. Add tofu and heat long enough to just get it up to soup temperature.
3. Garnish with the chopped green onions and serve.
My mother always gave me miso soup when I was sick.
Storage: If you want to have miso soup over a few days, put miso only in the portion of the vegetable soup that you wish to eat at that time. It keeps better without the miso in it.
Wakame: Wakame is a strong seaweed. It expands to many, many times its dry size when re-hydrated. It is strongly flavored, be very conservative the first time you use it. Most health food and Japanese/Asian stores sell it already cut into little 3/4 squares and dried into tiny crumbles. This is the best kind to use. If you buy it in sheet form you will have to hydrate it and then cut it into squares which adds time to the recipe.
Miso: There are many, many kinds of miso. The white miso sold in many stores is akin to white rice. Brown miso is akin to brown rice. Which you use is entirely up to your taste and nutritional inclinations. Some people feel hatcho miso is the best nutritionally. Many people feel that cooking miso destroys the favorable digestive enzymes, but two people whose opinions I really respect are in favor of cooking the miso into the soup for a short period of time (1 minute).
Daikon: Most Japanese people like their daikon pretty soft in miso soup.