Make the dashi by making cuts into the piece of kombu kelp (or snapping it into a couple pieces) and placing it in a medium pot/pan with the water. Warm over a medium-low heat to slowly bring it to a simmer (it will take probably around 10 minutes). Remove foam from top as it appears.
While you are making the dashi, cook the soba noodles according to the packet instructions (typically add to a pot of boiling water and and simmer for around 5min then drain).
Once the water with the kombu simmers, remove the kombu then add the bonito flakes. Bring back to a simmer, cook for 30 seconds then remove from the heat. Let the bonito flakes settle to the bottom then strain. (You can skip these steps if using instant dashi/ready made but use good quality.) Keep warm if noodles are not ready yet.
Finely slice the green onions using the white and light green part.
Add the soy and mirin to the dashi and mix in. Divide the drained noodles between bowls then pour over the soba noodles in the bowls. Top with sliced green onions and any additional toppings you choose.
Video
Notes
As mentioned above, the most basic topping is simply sliced onion, but you can also add shrimp tempura, slices of kamoboko (fish cake), wakame and/or tempura flakes.