Here's some general rules:
1. If your produce spoils after just a few days, you might be storing incompatible fruits and veggies together. Those that give off high levels of ethylene gas—a ripening agent—will speed the decay of ethylene-sensitive foods. Keep the two separate.
2. Never refrigerate potatoes, onions, winter squash or garlic. Keep them in a cool, dark, dry cabinet, and they can last up to a month or more. But separate them so their flavours and smells don't migrate.
3. With the exception of leafy greens, fresh fruits and vegetables should not be washed before storing. Washing will hasten deterioration of the produce. It is best to wash produce just before preparation or eating.
4. Refrigerate fruits and vegetables in perforated plastic bags to help maintain moisture yet provide air flow. You can use a knife to make several small holes in a food-grade plastic bag.
5. Do you want some of your fruits to ripen faster (avocado – we're looking at you)? Place the fruit in a paper bag with an apple or banana and soon that fruit will be ripe enough to eat.
We've also got a super handy storage guide cheat sheet for quick reference.