In a medium saucepan, bring the water to a simmer. Add the white vinegar.
Crack the eggs into a small dish or ramekin.
Create a gentle whirlpool in the simmering water by stirring with a spoon.
Slip the eggs, one at a time, into the center of the whirlpool.
Let the eggs cook for 3-4 minutes, or until the whites are set and the yolks are still runny.
Use a slotted spoon to gently lift the eggs from the water.
Season with salt and pepper.
Serve the poached eggs on toast or English muffin, if desired. You can also add butter or olive oil, or garnish with fresh herbs or chives for extra flavor.