The potent, sulfury aroma of onions is one of the most universal cooking smells. Onions are used in almost all of the world's cuisines, lending their savory bite to a wide range of dishes. The characteristic smell and flavor of the onion family is caused by complex sulfur compounds that are intended to deter animals from eating them. Humans, of course, eat them with gusto precisely because of those compounds. As enjoyable as onion flavors are, sometimes they can be overpowering, especially when raw. Because of this, cooks have developed many ways to tame their aggressiveness.
Refrigerate your onions for a day before use. Onions don't need refrigeration, they'll store for months in a cool, dark place. However, chilling the onions before cutting them makes their volatile aroma compounds less volatile.
Slice your onions with the sharpest, thinnest knife blade you've got. The potent sulfur compounds are caused when the cell walls are cut or crushed, allowing previously-separated chemicals to react. Thin, sharp blades cause less damage and therefore affect fewer sulfur compounds.
Soak sliced or chopped onions for five to 10 minutes in milk or lightly-salted water, then drain and rinse before use. This technique draws out the sulfur compounds, leaving the onions milder.
Rinse sliced or chopped onions under cold running water for one to two minutes. This washes away the sulfur compounds created during the chopping process, leaving the onions milder.
Blanch the onions by pouring boiling water on them for 30 seconds, then pouring it off. The onions will still taste raw, rather than cooked, but will be much milder.