Pour 2 qt. water into a deep 10-inch skillet or saucepan. Add vinegar and salt; heat the water to simmering.
Break 1 cold egg into a small bowl. With the bowl near the surface of the water, gently pour in the egg. Repeat with 3 more cold eggs, adding them in a clockwise direction so you can remove them in the same order. Adjust the heat to maintain a steady simmer.
Simmer the eggs, undisturbed, to desired doneness, about 3 minutes for a runny yolk and 5 minutes for a firmer one.
Using a slotted spoon, remove 1 egg at a time, starting with the one that you added to the water first. Transfer the eggs to paper towels to drain.