Several people I know have asked my opinion about chopping onions. The first inquiry I get is always how to chop an onion without crying. The only way I know to prevent the iritation of the eyes is to wear contacts. When you cut into an onion, it releases an enzyme that reacts with the water in your eyes. The enzyme and the water react and create an acid which iritates the pupil. It doesn't iritate the white of your eye and because the pupils are completely covered by the contacts, you can cut an onion without any problems. But not everyone wears contacts.
So the only other way I can think of to prevent eye iritation while chopping an onion is to do it as quickly as possible and with a sharp knife. Onions are a bit cumbersome with the papery out layers, the layers of flesh within, the root and the roundness of the vegetable (round things like to roll!). It can take a while to chop an onion which will make you take several visits to the freezer to cool off your eyes. So I'm here to teach you how to chop an onion quickly and efficiently. You may still cry, but it will be over with quickly since you'll be an onion-chopping master.
Place your onion on your chopping board. Make sure you use a good knife.
Chop your onion in half from the top to the bottom.
Lay each half on your cutting board, cut-side down. Cut off the top bit of the onion like in the picture above. Make sure you cut off the top part and not the root. It's important for the root to stay on.
Remove the papery skin of the onion. Leave the root on! Cut into each half twice creating 3 large slices. If your onion is small, cut into each half once to create 2 large slices. Do not cut all the way through. Leave the root on!
Take your knife and cut slits in the other direction. Do not cut all the way through the root. The onion half should stay together. Leave the root on!
Now run your knife across the onion half in the other direction until you get to the root. Throw out the root.
Voila! Chopped onions without tears (or at least with very few).
*You can dice or mince by creating more slices lengthwise and more slits in the other direction. Or you could take the chopped pieces and run your knife over them holding the tip of the knife on the chopping board and lifting the knife up and down, chopping as you go.