Hi Draytonsue and welcome to the Forum.
You're right to wonder what will help keep the run floor clean and sweet, especaially if part of it is uncovered and thus liable to get wet and muddy in winter. As Bickerton says, a good covering of woodchips will help - sometimes you can get these quite cheaply or even free from a local tree surgeon. Other options are bags of shredded hemp or similar, such as Comfibed or Aubiose, which are more absorbent than woodchippings.
If the run has an earth floor, the hens will dig mud up into it whatever you use, and this will be messier under the uncovered end. One way to prevent this is to cover the base with permeable weed proof membrane before you put down any sort of bedding on top. This will at least prevent the birds from scratching mud up into the bedding muddy from below, but they will still enjoy digging in the chippings and will have a soft, well-drained surface to walk around and sit on.
However., of course it will also get dirty and smelly unless you try to pick up the droppings as part of your daily routine. Done regularly, the floor covering will stay relatively clean for much longer and the run will be pleasant to walk in, for both you and the birds. It only takes a few minutes, just go round with a bucket and wear rubber gloves. This is much easier and more effective under covered areas that don't get rained on, of course.
If you don't want to cover the floor with membrane, and the woodchip gets very messy, you will need to dig it all out regularly. You can then dig in some sanitising powder (Stalosan) before putting down clean bedding.