If you need only 1/2 of onion, save the root half. It will last longer.
No need to shed tears while preparing onions. Peeling them off in water should do the trick.
If you stick you tongue out while chopping onions it will stop you crying. Alternatively, chop the onion close to a running tap. Apparently the chemicals in the onions go for the nearest source of liquid.
Rub your hands with vinegar before and after slicing onions – this will eliminate the smell.
If you forget to do the above – When peeling onions and the scent is on your hands, just run the cold water and rub hands with olive oil soap.