I once resorted to wearing ski goggles in a desperate attempt to avoid the dreaded onion tears. This was before I learned that such extreme measures were unnecessary (thank God, as it made for a rather unattractive aesthetic statement). There are many, many tricks out there – some positively nutty, including chewing bread, or holding a lit match between your teeth – but my advice is simple: use a sharp knife, and keep those onions in the fridge. Chopping breaks the onion cells, releasing sulfides that react with our eye fluids to cause the sting; tears are the eyes’ attempts to get rid of those nasty chemicals. A sharp knife cuts more efficiently than a dull one, smashing fewer cells, and the cold temperature decreases the volatility of the sulfur compounds; hence, less stinging. If that still doesn’t work for you, don’t give up on onions altogether: the more you chop, the less sensitive your eyes become.
To peel an onion, cut a thin slice off both ends. Make a thin longitudinal slice through one layer of onion; the peel should now come off easily.