Place Potato (3 pound) in a pot with hot water and Salt (1 teaspoon). Bring to boil and cook potatoes for about 10 minutes, until just tender. Do not overcook.
Into a serving bowl, add Mayonnaise (1 cup) and Pickle Juice (1/2 cup). Whisk until smooth. Add Onion (1) and Dill Pickle (3), then stir to incorporate.
Drain the potatoes when tender and add them to the dressing in the serving bowl. Mix gently. Season with Salt and Pepper (to taste) and Dried Dill Weed (to taste).
Serve hot, warm, or cold. The longer you let it stand, the more flavor develops, but it does taste great immediately.