To avoid your eyes from "tearing" when cutting large amounts of onions, put the peeled onions in the freezer for 15 minutes before cutting. Time carefully: do not let the onion get too hard in which case it may make you work a little harder to slice, dice, etc. The "flash" of cold prevents the release of sulfuric acid which is the compound in the onion that makes your eyes tear. When finished cutting the onion into the shapes you want - slices. dice, etc. - allow the onion to come to room temperature before using. Freezing in this manner will not affect the flavor of the onions.
Making guacamole or salsa? Tame the "heat" of chopped onions by running boiling water over them just before adding them to your preparation. This treatment will make them more mellow.
Wiping your cutting board with vinegar before cutting onions will help prevent your eyes from watering when you cut them.
To remove garlic odor from your hands, rub them, vigorously, on stainless steel sink or other stainless sink items, eg; faucets, for 30 seconds before washing them