1) Cut the onion in half lengthwise, going through the pointed end and root. Peel off the papery skin to get to the shiny layers, leaving the root intact or the juices will begin to bleed and cause you to cry.
2) Make a series of parallel vertical cuts down the length of the onion, stopping just before you hit the root.
3) Hold the onion steady and make two horizontal cuts through the onion, again stopping before you hit the root.
4) Now hold the onion like a tennis ball to keep it together. Pushing down with your index finger, middle finger and ring finger on top and thumb and pinkie off to the sides. Keep your middle finger slightly ahead of the other two fingers, using your knuckle to guide the knife to make repeated slices, moving your fingers back closer to the root as you go along.
5) You should have a pile of nicely diced onion and a root which you can cut off more or set aside for vegetable stock.