Wash the potatoes, and cut into equal-sized pieces.
Place in a saucepan, and cover with water. Bring to a boil.
Once at a boil, simmer until tender. After 10 minutes, test, and keep testing every few minutes, until just barely tender. DO NOT OVERCOOK, or the salad will be mushy.
When the potatoes are ready, drain them. Then let them cool enough so that you can handle them.
Peel the potatoes, and slice them into ¼ - ½ inch slices.
Drizzle vinegar over the potatoes, enough to coat all the pieces.
Drizzle oil over the potatoes, enough to coat all the pieces.
Let sit until cool.
Add chopped onions, chopped celery, and chopped parsley, tossing a little.
Serve, and enjoy.