First, take off any papery or blemished outer layers, so you're left with a pearly outer layer.
Then, cut off the non-stem/root end. (Cut off the end toward the right in the picture above.)
Next, you will want to bisect the onion from end to tip, through the root section. The onion will lay nicely on your cutting board because you've made a flat bottom for it in the previous cut.Take one of the halves and slice almost all the way from root to tip again, this time making radiating cuts out from the center. Another view.Finally, rotate the onion half 90 degrees, and make small vertical slices from the tip toward the root. Stop slicing when you are somewhat near the root end, and you don't have much for your fingers to grasp. Please use caution as you are chopping, so as not to injure yourself with the knife.
As you can see, you have a beautiful finely chopped onion. If you want to be technically correct about terminology, what you see pictured above is a minced onion. A diced onion would be more medium sized cuts, and chopped onions are the largest cut at about 1/4" chunks.
Some believe that keeping the root end of the onion mostly intact will reduce the amount of irritation to the eyes. Others say you must wear goggles. Others chew spearmint gum while chopping. Some chop their onions under running water. Other ideas: use a fan to blow the irritants away from the cutter, use a very sharp knife blade, chill onions before cutting, get some other guy to do it. Really, some people try to pawn it off on some other poor soul. Try each method, and see what works best for you.
Here are a few interesting tid-bits of onion trivia.
By the way, my model onion above was used to make black bean enchiladas tonight, somewhat as described here. ¡Buen provecho!