Home of Rhett & Link fans - the Mythical Beasts!
Cooking the onion inactivates the enzyme, so while the smell of cooked onions may be strong, it doesn't burn your eyes. Aside from wearing safety goggles or running a fan, you can keep from crying by refrigerating your onion before cutting it (slows reactions and changes the chemistry inside the onion) or by cutting the onion under water.
The sulfur-containing compounds also leave a characteristic odor on your fingers. You may be able to remove or reduce some of the smell by wiping your fingers on a stainless steel odor eater.