Wash and peel the potatoes, cut them in half, and cover with cold water. Add salt and set on the stove. Bring to a boil and cook for 3-4 minutes. Drain and dry thoroughly.
Heat olive oil in a pan and add drained potatoes. Fry until lightly browned on each side, about 7 minutes. Remove from the heat, add the garlic, and mix. Set aside to cool.
Transfer to a bowl, season with black pepper. Add chopped dill and mix. Slice the radishes and onion very thinly and add to the bowl of potatoes. Add the arugula.