Scrambled eggs are a cinch to make compared to the poached variety. You know exactly when scrambled eggs are done when they reach the texture you prefer. There's no guessing as to whether the yolk is hard or still runny. Fresh eggs are better for poaching because the whites cook up firmer and don't feather off into the simmering water leaving the yolk to fend for itself.
Hard poached eggs have a firm yolk similar to hard-boiled eggs. How long you poach the eggs determines how cooked the yolk is and its firmness. Since eggs should be refrigerated until they're used and different refrigerators are set to different temperatures, how cold the eggs are before they start cooking varies as well.
The size of the egg affects the cooking time as well. Sacrifice a few eggs to determine how many minutes it takes eggs from your refrigerator to cook firmly. Start with three minutes and increase by one-minute intervals. Large eggs should poach to firm by five minutes. Use your finger to push on the egg yolk underneath the white. If it gives, it's not hard cooked.
Vinegar and Salt
A tablespoon of vinegar added to the water keeps the egg whites in one mass rather than spreading out. The acid in the vinegar coagulates the proteins on the outside of the whites so they don't fan off into the water. Salt has the opposite effect. While you may add salt to season the water to cook potatoes and pasta, don't add it to water for poaching eggs.
Simmer Don't Boil
Bring the water to a boil then lower the heat so bubbles barely break around the surface of the water. Break the eggs into separate cups. This keeps the egg together as you slide it into the water rather than cracking the egg and dropping it in from above the pan. Breaking the eggs into separate cups lets you throw any bad eggs out. As soon as all the eggs are in the pot, cover and simmer.
Poach eggs so they have a neat rounded shape with the egg whites close to the yolks. Swirl the water in a pot with at least 3 inches of water. The pot should be at least 5 inches high so the water doesn't swirl over the edge while you're stirring. The centrifugal force of the swirling water keeps the white close to the yolk. Alternately, set an egg ring, mason jar rim or a ring made from a cleaned bottomless and topless can of tuna fish. Hold the egg over the ring and gently drop in.