A sharp knife makes cutting an onion (or shallot) much safer and also releases less of the substance that makes your eyes water. If you are storing raw chopped onions in the refrigerator, cover the container with aluminum foil so the odor doesn't affect other foods.
STEP 1 - With a paring knife, cut off the top end from the onion. Slit the papery outer skin lengthwise and peel off and discard it.
STEP 2 - With a chef's knife, cut the onion in half lengthwise.
STEP 3 - Place each half cut-side down. With one hand held flat on top of an onion half, make three or four horizontal cuts toward the root end (but don't cut all the way through). The size of the slices will determine the size of the final dice.
STEP 4 - Make several vertical cuts down through the top of the onion.
STEP 5 - Finally, slice across the onion, guiding the knife with your curved fingers, to make uniform dice.
STEP 6 - To chop the onion into smaller pieces, hold the tip of the knife down with one hand and lift the knife up and down with the other, moving it through the onions and occasionally gathering them back together, until they are chopped as finely as you desire.