Onions

I generally just go ahead and chop the whole onion. Measure out the amount I need, and then measure out the amount left and write what that is on a small freezer baggie. Put the chopped onion in the marked baggie and into the freezer. I do that with celery, carrots and peppers as well. It's amazing how handy those little baggies of chopped veggies come in when you're in a rush.

I use a medium or small sized ziplock bag. My half used onions stay firm and crisp for quite a while in the fridge like this

You can chop the rest of the onion and freeze it in a small container.
Or you can do the simplest thing in the world: Put the cut edge of the onion on a small plate or lid -- a flat surface, and put it in the fridge. In our house we use lots of onions, so it will only be there a day at most. The smooth dry outer shell of the onion won't dry out in such a short time, and I've never had trouble with onion smell transferring to other foods.
I have heard/read that onions and potatoes should not be stored together -- is that true?

This won't work for every recipe calling for small amounts of onion, but usually, I just use a shallot or two instead of onion (no onion leftovers) OR I just take a smallish onion and use the whole thing. Otherwise, the plastic wrap trick will work just fine.

Wrap cut onions with non-permeable plastic wrap (Glad Cling Wrap or Press 'n Seal) and store in the refrigerator until needed. Discard a thin slice of the onion before using the rest as the cut / exposed portion can take on a bitter flavor after a brief time.

This is a good example of LDPE's superiority over PVC-based plastic wraps.

Dang you lack of "Edit Button"....I should have mentioned you snip off the onion you use below the knot. Onions will keep several months this way in a cool dark place.

Wrap tightly in plastic wrap and store in the 'fridge.

To store onions, whole, for long periods of time. Use some woman's nylon stockings. Put in a onion, tie a knot, add another, and knot---repeat. Then hang them up in a closet or good cool pantry.

I don't that anymore as I get strange looks when buying panty hose.