Rinse and remove any bad spots or eyes from the potatoes. Don't peel.
Place potatoes n a large sauce pan and cover them with cold water by two inches.
Slowly bring the potatoes to a boil. Cook them until just about done. When you insert a knife into the potato and it slides out somewhat easily, those potatoes are done enough for potato salad. Depending on the size of the potatoes, plan on 30 - 45 minutes cooking time.
Drain potatoes in a colander. Remember, when you drain them in the colander, they're so hot, they'll continue to cook for a few minutes more. The skins will peel off easily since they're cooked, or I like to leave skins on.
Meanwhile, chop your vegetables. Place them in a large bowl.
When the potatoes are cool enough to handle (they'll should still be hot) With a knife, coarse chunk, or cut the potatoes in half, while adding them to the bowl with the celery and onions. Let sit for a couple of minutes before stirring. I like to do this to steam the vegetables and let the flavors marry a little bit.
Top with mayonnaise and a tablespoon or more of mustard. This all depends on your taste preference. Add the olives if using. With a large spoon gently fold the potato salad together. At this time I start adjusting the flavors, adding more mustard and mayo, if needed, for both texture and flavor.
Remember, the potatoes were boiled in salty water. Taste before adding salt and pepper.Top with sliced hard boiled egg if you'd like. Remember, those eggs will slice cleaner if they've been sitting in the refrigerator for a couple of hours after boiling. Refrigerate at least one hour before serving.