All this dashi talk got me hungry for udon.
Dashi can either be homemade by steeping any of the mentioned ingredients (dried kelp, skipjack flakes, bonito flakes, shiitake mushrooms, etc.) or prepackaged packets of dashi mix in water. The dashi is then mixed with mirin and soy sauce and then simmered to make the soup broth. Your udon noodles can also be homemade with nothing more than all-purpose flour and salted water, but it takes practice to get good noodles. Homemade Dashi should come out looking goldish if you're using the fish flakes (this is the only type I've made), remember to skim it. The leftovers can be reused like drying the fish flakes into a rice seasoning and eating the mushrooms.
A nice broth makes from:
2 1/2 cups dashi (either homemade or from a packet)
1 tbsp mirin (can substitute with sake)
1 tbsp soy sauce (usukuchi for a lighter color but it's just an aesthetic preference)
1/4 tsp salt (or 1/2 kosher salt if you got it)
1 tsp sugar (could skip since mirin has sugar in it already, but add a little more if subbed with sake)
Bring to just a boil then drop it low and cover to simmer.
Your noodles can be udon or if you're ghetto you can use any wheat pasta. Cook according to instructions.
Take the noodles out and strain them and optionally rinse with cold water, then put them into your serving bowl and fill with the broth.
If Kitsune udon all you need left is some aburaage which may be tricky if you don't have an asian grocer nearby. If it's prepackaged you need to squeeze it like a sponge to get all the oil out, then serve on top of the udon with choice of garnish like green onions and shichimi togarashi (seven spice) if you want it to have a spicy hit. You'd also serve the shiitake mushrooms here if you used that for making the dashi.