Into a mesh strainer, crack each egg one at a time to strain some of the excess egg white, about 20 to 30 seconds. Pour each egg into individual small bowls.
Fill a Dutch oven or large pot halfway with water, about 6 cups, and bring to a boil. Add the vinegar. Reduce heat to a gentle simmer so the water is steaming and small bubbles barely break the surface.
Gently drop one egg into the water at a time, leaving space between them. Cover pot, remove from heat, and let stand until whites closest to the yolk are just set and opaque, about 3 minutes (or 4 minutes for medium-cooked yolks or 6 minutes for hard-cooked yolks).
If the whites are not set after 3 minutes, continue checking every 30 seconds. Using a slotted spoon, carefully lift each egg out and drain over the water. Pat dry with paper towels if desired season to taste with salt and pepper, and serve.
Notes
Eggs: Because they have thicker and firmer egg whites, fresh eggs are best for poaching.
Vinegar: The acid helps the egg white coagulate as quickly as possible. Lemon juice can be substituted for vinegar, but may change the taste of the eggs slightly. If you have it, opt for white distilled vinegar for poaching eggs.
Yield: This method for how to poach eggs creates 4 eggs. Scale up or down as needed, cooking no more than 4 eggs at once in the same pot.
Storage: Store poached eggs submerged in cold water covered in the refrigerator for up to 2 days. Reheat in a pot of warm water for a few seconds until heated through.