ImmaEatThat is right. I will add that I wash my herbs and then chop them up and add it to something I am cooking. Then, I do the paper towel business.

All recommendations above are good.

I will add that you may ripen many fruits and vegetables in a paper bag. Be careful. Some ripen quick, like peaches, which is handy. Also, a window sill is a blessing.

Tomatoes are best stored upsidedown as the blossom side is where there is the most moisture loss. Definitely not in the fridge for tomatoes. For many other things the trade off in shelf life vs. quality is not that extreme.

Damp paper towels keep produce longer, refreshing them instead of drying them out.

With herbs, also wrap in a damp paper towel.

Also, make sure your produce is dry. There is nothing worse than having lettuce heads/herbs sitting in a lake of water. Summer items like tomatoes need to breathe, and should have very little water contact until needed. Store in a cool dry place, with some spacing in between. If you have a rack, like a sheet pan with parchment paper and lay tomatoes on them. If you detect a bad one, separate from others. This can be with peaches, plums, nectarines, avocadoes, cherry tomatoes. It is also quite visually appealing.

I agree with Antonia James and Loves Food Loves to Eat comments. Adding to foods I don't refrigerate are potatoes as the cold will turn the starch to sugar, thus affecting the flavor. Tomatillos, the green tomatoes in a husk, are in the tomato family and shouldn't be refrigerated for the best flavor if you're going to use them fairly quickly. If not, you can remove the husks and place in a plastic bag unsealed and they'll keep for as long as 3-4 weeks. They'll only last up to 2 weeks in the frig with the husk on. A local strawberry grower told me the best way to store berries is in the refrigerator in a single layer (assuming you have the space to do that). Berries don't continue to ripen after they're picked, they just get soft. So the bottom berries are going to get mushed, inviting decay faster. And lastly for my leafy greens, I wash them when I bring them home (or pick them from the garden) and put the leaves in an unsealed plastic bag with very damp paper towels. This keeps them nice and crisp for muuuuuch longer.

I agree with Antonia on the tomatoes. For other produce, my CSA-farm suggested storing things in the fridge in large ziplock bags. I find that leafy greens, carrots, cherries, and other farm-fresh produce from the CSA (which generally goes bad so much quicker) lasts several days longer in a ziplock!

Frankly, with one exception, I don't think there is a single proper way to store any fruit or vegetable . . . it depends on which you are talking about, how recently it was picked, and the temperature and humidity of your kitchen counters, pantry and refrigerator. The single exception is tomatoes. The best way to ruin a good tomato, almost instantly, is to refrigerate it. Depending on how ripe a tomato is, I'll either store it on an open shelf (a warm place in my kitchen) or in my cool but not cold pantry. Then I eat or serve it as soon as I can. Blueberries picked off my bushes can sit out for three or four days, or longer, but then, I live in the San Francisco Bay Area, where our summers are quite temperate. ;o)