In a medium saucepan, bring 6 cups of water to a gentle simmer over medium heat. Avoid a rolling boil.
Once simmering, add 1 tablespoon of distilled white vinegar to help the egg whites set quickly.
Crack 4 fresh eggs into separate small bowls for easy transfer and to ensure no shell pieces get in.
Using a stirring spoon, create a gentle whirlpool in the simmering water to help the egg whites wrap around the yolks.
Carefully slide each egg one at a time into the center of the whirlpool, spacing them out to prevent sticking.
Allow the eggs to cook undisturbed for 3-4 minutes; 3 minutes for runny yolks or 4 minutes for firmer yolks.
Use a slotted spoon to gently lift the poached eggs out of the water and let drain briefly on a paper towel.
Season with salt and freshly ground black pepper to taste. Serve immediately over toast, salads, or your favorite dish.