Start by finely chopping the red onion and celery. Set aside.
Place the potatoes in a large pot with the peelings still on. Add enough water to where they are covering the potatoes and bring to a boil. Boil for 20-30 minutes.
After the potatoes are done boiling, drain them in a strainer. The peelings should be starting to pull back and the potatoes should be extremely tender. Allow the potatoes to cool before peeling, about 30 minutes.
Using a knife, remove the peelings off the potatoes. They should be very easy to cut off.
Using a knife, cut the cooked potatoes into large chunks. It's ok if the potatoes start to fall apart while cutting.
Put the tender chunks of potatoes in a large bowl.
Add ¾ cup of mayonnaise, 3 Tablespoons of mustard, 4 Tablespoons of relish, ¼ cup chopped red onion, and ½ cup of chopped celery, and salt and pepper to taste.
Mix until well combined. Taste test to ensure it’s at the right level of flavor you want. Add more salt, pepper, or any other ingredient if you think it needs it.
Store in the refrigerator for 4-6 hours before serving.