Q: How can I maintain a clean, enclosed run if I can't free range my birds?
A: Due to the number of predators in some rural areas, some pet chicken owners don't allow free ranging. Other times, an enclosed run in a small suburban yard is the only way to keep chickens safe and contained so they don't run into traffic or make themselves the target of neighborhood dogs. The problem can be that the chickens quickly forage all the green out of their run, and then droppings accumulate on the hard dirt. Cleaning can be difficult, because moist droppings do not rake up too well. In these situations you may want to try adding some bedding.
What bedding you will want to use for an enclosed pen will probably depend on your coop's exact situation. Many people like to use pine bedding, but that will work best if the run is covered and sheltered from rain and snow. For instance, in the Garden Coop (pictured below), pine bedding is used in the enclosed run. That's do-able because the run is sheltered from the rain. In those circumstances, the pine bedding helps to dry out the droppings as they fall, so the run is easier to clean effectively.
But if your run is exposed to rain and snow, you might instead prefer to use something like sand in your run, since pine shavings would get wet, hold the moisture, and begin to rot. Sand drains and dries more quickly than clay, and will probably be easier to rake.
That said though, having your birds confined permanently to a run that's too small to maintain any green grass is not an ideal situation. Not only will you not be getting the full benefits of keeping your own hens--remember, eggs from chickens raised on pasture are far healthier!--but you will also have more problems with aggression and illness in your flock. Illness can spread more quickly when the birds are confined closely together. And birds that are bored because they have nothing to forage for will spend more time enforcing and reinforcing the pecking order, which can lead to feather picking and injury.
For that reason, if you are genuinely unable to let your birds range in a large area, you may want to either expand the enclosed run area they do have access to, else keep few enough birds that the existing run will be large enough for them, or range them part time in a larger area when you're around to supervise and keep them safe.