How do I properly poach an egg without it falling apart?

The key is using fresh eggs, since older eggs have thinner whites that spread and fall apart. Bring water to a gentle simmer, not a rolling boil, and add a splash of white vinegar, which helps the whites coagulate faster. Create a gentle swirl in the water with a spoon, then slide the egg in from a small bowl held close to the surface. The swirl helps wrap the white around the yolk. Cook for about 3 minutes for a runny yolk. Avoid disturbing the egg while it cooks. Lift it out with a slotted spoon and blot on a paper towel. The fresher the egg and the gentler the simmer, the cleaner your result will be.