Random bits of advice from friends, family, and cooking shows that have proved inordinately helpful, for any newbie cooks out there who might find them useful.
Chopping an Onion
Slice the top and bottom off the onion, cut in half lengthwise (with the grain), and peel.
Set one half face down, turned so that the top or bottom is closest to you. Slice vertically on an angle, starting at the right side of the onion, so that you create a series of wedges.
Turn the onion 90 degrees, and slice again, this time crosswise. The rings will fall apart into squares. (You can do the same with shallots and leeks.)
For some reason, this way of cutting an onion usually doesn't make me tear up (maybe because the cut sides stay together longer), it's quick and easy, and makes it simple to chop very evenly.
After cutting the bottom off the clove, lay a chef's knife or cleaver horizontally, flat against the clove, with the sharp side of the blade angled very slightly downward. With the heel of your hand, thwack the top of the knife hard enough to slightly mush, but not completely smash, the clove of garlic. The peel should pull off easily (if not, try hitting it a little harder). Make sure you keep the blade of the knife angled down slightly and your fingers up and out of harm's way.
The easiest way to prepare garlic, by far. Cut the bottom off the clove, as above, and again hold the knife flat across and smash down with the heel of your hand -- only this time, really smash. Make sure the sharp end is slightly tilted downward, and that you hold your fingers up out of the way. The garlic should smash out of the skin and look, to use a technical term, well-smooshed. It's okay if it breaks into pieces. To cook with it, heat a pan over medium heat, pool a little olive oil in the middle, and add the smashed clove, and then drizzle a little more olive oil over the top. Simmer in the oil until golden.
If you need to cut or chop leafy greens like kale, bok choy, or Chinese cabbage, it's often easier to slice first and wash second rather than trying to wash and dry the whole leaves and then cut each one. Place the whole head on a cutting board and slice crosswise, starting from the top (so that the bottom holds the leaves together). Toss the sliced greens in a salad spinner to easily rinse and spin dry.
Shelling Fresh Fava Beans
For speedy shelling: Pinch each bean through the pod between thumb and forefinger, and push out through the shell into a bowl. For faster peeling: Blanch the beans, then break open the fattest part of the skin and pinch the opposite end to shoot the bean out. See this post for details.
Storing Fresh Herbs
Keep herbs fresh for up to a week in the fridge by simply snipping off the bottoms of the stems like you would fresh flowers and setting them in a mug or glass with about an inch of water at the bottom. Cover the top loosely with a plastic bag before refrigerating. (The best part about this trick for me is that I'm much less likely to forget about the parsley when it's sitting front and center than when it's tucked away in the depths of a vegetable drawer.)
Peeling and Seeding Pomegranates
To more easily seed a pomegranate, slice them in half (or start to slice, and pull apart the rest of the way) and dunk them in a bowl full of cold water. Let soak for awhile (anywhere from an hour to overnight) to soften, then gently break each piece in half and re-immerse. After a few minutes, each piece should pull apart easily to reveal whole pockets of seeds that you can gently push out with your fingertips.