Find the top and root ends of the onion. Lay the onion on its side and cut the top off. Place the onion on this flat cut with the root pointing up. Cut trough the center of the root so that a bit of root remains on each half of the onion after it is cut. This will help the onion stay in one piece as you make the cuts. Peel the onion of all the outer skin.
Place onion on a large cutting board. You will cut into the onion through the side where you cut the top off. If you are right-handed, point the cut side to the right. Hold the onion steady by pressing down on the top with your fingertips. This will keep your fingers out of the way of the blade. Hold the knife with the blade parallel to the counter and place the part of the blade closest to the handle in contact with the onion. Now pull the knife back toward you, slicing the onion, but not all the way through! Repeat this step making as many horizontal slices as you like. The more you make, the smaller the dice will be.
Now turn the onion so the cut topside is facing you. Curl your fingers a bit to keep them out of the way and start slicing from the top of the onion down to the counter starting from the right edge, assuming you are right-handed. Move your curled fingers across the onion and follow with the knife, making slices as you go, but do not cut through the root! Again, the more slices, the smaller the dice.
Turn the onion back to the first position with the cut topside facing the right, curl your fingers again and cut through the onion from the top to the counter parallel to the very first cut. Move your fingers back toward the root, following with the knife, making slices as you go. This time everything will fall free and you will have beautifully diced onion. Discard the root.
One Last Thing
If you are only using half an onion in your recipe, do not peel the onion after cutting it in half. Wrap it tightly and refrigerate for optimum freshness.