Most tips I've read recommend you store your veggies in plastic bags. I'm not a huge fan of plastic and I recommend investing in some good food storage containers (preferably made of glass). This makes your veggies highly visible and will keep them fresh for a whole lot longer than just sitting on the shelf.
Wash your veggies when you are ready to use them. I've found that the little amount of dirt helps preserve them.
Wilted greens and lettuce are often just dried out which can still occur even if the greens remain in constant refrigeration. Submerge the wilted greens in cold water by placing them in a dish, filling it with water, and putting it in the refrigerator overnight. It should bring your greens right back to life.
Arugula: Keep arugula refrigerated (32-36 degrees F), stored in a tupperware, away from fruits to avoid deterioration.
Beets: Keep beets refrigerated (32-36 degrees F), The stems can be removed and stored separately (beet greens are delicious!). The beets do not need to be in a container, but I've found they last longer when they are.
Bok Choy: Keep bok choy refrigerated (32-36 degrees F), storing in a container.
Broccoli: Keep broccoli refrigerated (32-36 degrees F), storing in a container to help retain moisture.
Cabbage: Store cabbage in the refrigerator (32-36 degrees F), storing in a container.
Carrots: Keep carrots refrigerated (32-36 degrees F). Remove tops immediately and store carrots in a container. Sometimes you can even put a little water in the bottom to help them keep their moisture.
Cauliflower: Keep cauliflower refrigerated (32-36 degrees F) and store in a container. Discard any leaves or parts you will not be using. This helps the cauliflower retain moisture.
Celery: Keep celery refrigerated (32-36 degrees F) and store in a container. Chop off leafy part at top and discard or set along side celery in container. This will help the stalks retain moisture.
Corn: Keep corn refrigerated (32-36 degrees F) and store in a container. Leave husks intact, but check for organic worm and remove before storage. Do not fear the worm. Its sole interest is your corn and it's a beautiful part of this crazy world.
Cucumbers: Refrigerate your cucumbers, but eat them as soon as possible. I suggest keeping them off the bottom shelf, which is usually the coldest part.
Eggplant: Eggplant generally should not be refrigerated because the low temperatures can damage the texture and flavor. It's recommended to store at room temperature, although it may be kept in the refrigerator 1 to 3 days if used soon after removal. Keep it in a cool spot, away from direct sunlight. Avoid putting it in a sealed container which can increase decay.
Fava Beans: Keep fava beans refrigerated (32-36 degrees F) and store in a container in whole shell until ready to use.
Fennel: Trim off parts you do not plan on using. Refrigerate at (32-36 degrees F) and store in a container.
Greens: Kale, Collards, Chard, Mustard Greens - Refrigerate at (32-36 degrees F) and store in container to keep from dehydration. See above to revive droopy/wilted greens.
Green Beans: Refrigerate at (32-36 degrees F) in container to keep crisp.
Kohlrabi: Refrigerate at (32-36 degrees F) in container to retain moisture.
Leeks: Keep refrigerated at (32-36 degrees F). Trim off the green part. The white part is best for cooking and the green part can be discarded or used in soup stalks.
Lettuce: Keep lettuce refrigerated at (32-36 degrees F) in a sealed container. You can wash and prep lettuce before you put it in the fridge for ultimate convenience.
Onions: Store whole onions in a cool, dry, dark place away from potatoes. Always refrigerate cut onions in a separate container.
Peppers: Store whole peppers in a cool dry place away from fruits to avoid over-ripening. Always refrigerate the cut peppers and the same goes for whole peppers if you don't intend on eating them immediately.
Potatoes: Store whole potatoes in cool, dry place but do not refrigerate.
Radishes: Refrigerate at (32-36 degrees F) and place in container to retain moisture.
Snap Peas: Keep snap peas refrigerated at (32-36 degrees F) in a sealed container.
Spinach: Refrigerate at (32-36 degrees F) stored in a container. Our spinach will be washed 3 times and comes in a plastic bag which is great for storing as well.
Strawberries: Don't wash the strawberries until you are ready to eat them. Stack strawberries on top of a paper towel in a single layer. Put another paper towel on top and keep stacking if needed. This will keep the excess moisture from spoiling the berries.
Summer Squash: Refrigerate at (32-36 degrees F) stored in a container. The yellow squashes tend to degrade a bit quicker than the green zucchini. Use yellow squash first.
Tomatoes: Keep tomatoes at room temperature. Do not refrigerate, as it will make the tomatoes mealy and flavorless. If you cut into a tomato and need to refrigerate it, use it as quickly as possible.
Winter Squash: Store winter squash in a cool, dry place. Will usually last throughout the winter so it can be saved until last to eat.