According to gardening.cornell.edu, fruits and vegetables should be stored under proper conditions according to that specific fruit or vegetables set of conditions. As a rule of thumb, you will want to think about how the produce you purchase is stored or displayed at the grocery store and that will give you an indication of how to store fruits and vegetables at home.
A cold, moist condition for fruits and vegetables can be found in your refrigerator. Most refrigerators have a product drawer specifically designed for this purpose. Rinse your fruits and vegetables and then store them in your refrigerator's produce drawer. Fruits and vegetables that require this type of condition include apples, celery, lettuce and spinach.
Many vegetables require dry storage such as garlic, onions and some potatoes. A pantry or hanging produce basket provides the perfect storage for these types of items. Be sure to store these and other fruits or vegetables requiring dry storage out of the way and away from varied temperature conditions. Keep them at a consistent temperature daily to get the most out of your produce. Other types of dry storage can include a closet or even the garage.
Fresh herbs are another type of produce that require specialized storage. It is suggested to wrap fresh herbs in a damp paper towel and store in a plastic bag. You can also choose to put them in cold storage in your refrigerator drawer with the other produce.