I’ve tried many methods to poach eggs, but this one seems foolproof, from Julia Child via the NY Times:
Bring a small pot of water to a boil. Have a bowl of ice water at hand. Punch a tiny hole in the end of the egg(s). Gently place the egg(s) into fully boiling water for 10 seconds. Transfer the egg(s) to the ice water. Crack the egg(s) into a small bowl and slide into the boiling water one at a time. Turn off the water. Remove when poached to your satisfaction (for me, about 3 minutes).
My (also foolproof) method is to simply put a couple of tablespoons of vinegar in boiling water, drop in eggs, and out come perfect poachies.
Mine never do when I do that, John.