If you have plenty of drawer space in your kitchen, a drawer is ideal for storing dish cloths. The deeper a drawer is, the better, depending on how many dish cloths you have to store. Fold dish cloths to fit the space available, and place them with the fold toward you, which is especially useful if you have cloths that are all one color, making grabbing just one without disturbing the others easy.
Use an ordinary grocery bag to throw dish cloths into right out of the dryer. Folding them isn't necessary. The bag may be hung on a drawer or a door knob or even on a hook under the sink if you prefer the bag stays out of sight. You may also use a drawer or storage bins in the same way as long as they are easy and convenient to reach into to get what you need.
Stackable bins are good for storing dish cloths, among other things. If you are short on space, stack bins under your kitchen sink or on a shelf in a cupboard, and use them to store dish cloths. Additional bins may be used for towels, scrubbies and rubber gloves if you desire.
Install stick-on towel racks or hooks inside the kitchen cabinet door to hang up used dish cloths to dry. Ensure the water that drips from them will not hurt the interior of the cabinet. Or you can hang them over the oven door handle or on an organizer behind a door.
Change out or clean your dish cloth at the end -- or beginning -- of every day. Dish cloths are a breeding ground for bacteria. Soaking them in bleach and water will disinfect them, but frequent exposure to bleach may also cause them to wear out more quickly. A small stock of dish cloths, enough to get you between laundry days, is helpful and allows you to place each day's cloth into the hamper and start over with a clean one.