Start by cutting off the roots (but not the root ball) and the top of your onion:
Next, cut into the top layer of the skin of the onion from one end to the other. . .
Using the edge of your knife, peel back the corner from where you just cut, this will release the peel and you will be able to remove the whole thing in one swoop. . .
Cut your onion in half (you can see the little bit of the root ball at the bottom of this picture) . . .
Cut into the onion in a "sundial" pattern, cutting from the outside to the center of the onion. The trick here is to not cut all the way back into the root ball (notice how far back the knife is in the onion). . .
Now you can chop your onion without all the little parts slipping all over. Cut back to the root ball and discard the hard bit that remains.