Cats are very sensitive animals. If your cat is very sick, she may need your help keeping clean. However, you need to do this as gently as possible. Bath time can be traumatic for a healthy cat; for a sick cat, it can easily cause too much stress, making the cat even sicker. For a mildly soiled, ill cat you can use a dry pet shampoo. These are simply combed through the fur and will remove excess oiliness and dirt. If this is not sufficient and you have to damp clean a very sick cat, you can do so. You'll just have to take extra precautions.
Gather your supplies before bringing the cat into the room so she doesn't have extra time to get worried about what is about to occur. Create a comfortable place for her on a table by folding towels or clean blankets on the surface. If the room is cool, place the towels in a hot dryer for a few minutes before putting them on the table. Your cat will appreciate the extra warmth.
Fill a bowl or bucket with warm (not hot) water. Add a few drops of a mild pet shampoo to the water. Since you will be giving her essentially a sponge bath and won't be dipping the cat directly in water, the shampoo won't be as easy to rinse off so use it sparingly. Fill the other bowl or bucket with warm water for rinsing.
Place the cat gently on the towels. Use a soft brush to remove excess fur. If brushing upsets him and he resists, do not continue. Instead, pet him. Some loose fur will come off this way too. If feces or other debris is clinging to his hind end, clean this area first. If feces is still a little wet, use a cloth dampened in the water and shampoo mix to try to clean it off. If feces has already dried, cut off the fur it is attached to, if you can do so without hurting him.
Use a clean cloth, dampened in the shampoo and water to clean other soiled areas. If she has stains or debris around her eyes, nose or mouth, clean these first, especially if she appears to be disliking being washed. At least you'll get these important areas clean. You can come back at another time and clean other areas.
Wet a cloth in the rinse water. Rub it gently over all the shampooed areas. Dry the cat well with a towel. If the room is chilly or he is shivering at all, wrap him gently in a warm blanket or towel.