Most cooks tend to cut at least one end, and peel away the outer skin and layers until a sufficient tender core is uncovered, and the papery layers are removed. But, this actually exacerbates the problem by exposing too much onion—and fumes—before much work with it can be done. The objective is to not only lose as little onion as possible, but also to prevent cooking discomfort caused by the typical tears and sinus reaction to it.
Step2
By first peeling the entire onion before cutting, much of the smell is still contained and less apt to permeate the cook. Once the onion is peeled, hold it by the root or tail for the next step.
Step3
Still holding the root or tail, use a sharp knife to slice off the opposite end. Once the skin has been broken, proceed to slice, dice or otherwise cut into pieces the rest of the onion. Then add it to your dish, or freeze in a plastic bag for later use.
Tips & Warnings
You should experience minimal tearing and have an easier time of working with onions overall with this method.
Make sure to thoroughly wash your hands after working with the onion and especially before rubbing your eyes, or handling babies or pets.