Gather your ingredients, including potatoes, mayonnaise, mustard, vinegar, celery, red onion, salt, pepper, and optional additions like chopped hard-boiled eggs or fresh herbs.
Start by washing and scrubbing the potatoes thoroughly. You can leave the skins on for added texture and nutrients, or peel them if preferred. Cut the potatoes into bite-sized chunks for even cooking.
Place the potato chunks in a large pot and cover them with cold water. Add a generous pinch of salt to the water. Bring the water to a boil over medium-high heat, then reduce the heat and simmer the potatoes until they are fork-tender, typically about 10-15 minutes.
Once the potatoes are cooked, drain them in a colander and rinse them briefly with cold water to stop the cooking process. Transfer the potatoes to a large mixing bowl and allow them to cool completely.
In a separate bowl, mix together the mayonnaise, mustard, vinegar, salt, and pepper to create the dressing. Adjust the seasoning to taste, adding more mustard or vinegar if desired for extra tanginess.
Add the diced celery and red onion to the cooled potatoes in the mixing bowl. Pour the prepared dressing over the potatoes and gently toss everything together until the potatoes are evenly coated.
Cover the bowl of potato salad with plastic wrap or a lid and refrigerate it for at least an hour to allow the flavors to meld together and the salad to chill.
Once chilled, give the potato salad a final toss to redistribute the dressing. Taste and adjust the seasoning if necessary. Garnish with chopped fresh herbs, if desired, and serve cold as a delicious side dish or main course.