Prepare and cut potatoes, celery, onions and dill. (Alternately, you can also start with preparing the potatoes and chop the rest of the ingredients while they are cooking or chilling.).
In a large pot, put cut potatoes into water. Add 1 tablespoon of salt and stir. Bring water to a boil and reduce heat to medium, cook for 20 minutes or until desired firmness is reached.
While the potatoes are boiling, you can also boil the eggs by bringing water to a rolling boil, spoon each egg in, turn heat off and let them sit in the water for 10-12 mins.