I have a video that details the process (link at bottom), but in short:
The process is simple but keep in mind that there are dozens of varieties of kelp (kombu) and katsuo (bonito) that people use, so it’s easier to think in terms of ratio when making dashi. Keep notes as to the proportion and ingredients you use so you can learn how to adjust. Having said that, the basic ratio is 1 - 2 percent konbu and katsuo to water (I have a chef friend who uses 3% katsuo, so there’s a lot of personal preference involved).
10-20 grams konbu (dried kelp)
10-20 grams katsuo flake (bonito flakes)
Soak the konbu over night, but no more than 24 hours or the water becomes ‘slimy’.
Heat that water to the simmer and add your katsuo flakes. Keep the water under the boil and cook for no more than two minutes (if and when the katsuo sinks to the bottom of the pan, that’s the sign the dashi is finished).
Strain through a fine mesh sieve, paper towel, or coffee filter to remove any particulate (for the clearest possible soup) – do not press the solids.
Now you have dashi.
To make ‘soup’ for osumono (Japanese seasonal soups)
1 teaspoon light soy sauce
1/4 teaspoon salt
400ml of the dashi
add the salt and soy sauce to the dashi and bring to a simmer. Ladle into bowls of cubed tofu, poached fish, forcemeats or seasonal vegetables.