Remove all clothing, shoes and accessories from the cedar closet so the closet is completely empty.
Wear a dust mask to avoid breathing in any cedar dust. Wear a long-sleeve shirt and pants to keep the cedar dust from irritating your skin.
Sand the surface of the cedar closet with fine-grit sandpaper. This can be done by hand, but the job goes much more quickly with an electric sander. Rub the entire surface, including the ceiling if it's made of cedar, in order to freshen the cedar wood scent while removing surface dirt, stains or grime.
Wipe the entire surface of the cedar closet, starting at the top and working your way down toward the floor, using a dry cloth. Shake out the cleaning cloth frequently or change to a new cloth as you pick up more cedar dust. Continue to do so until you've removed all cedar dust from the closet surface.
Vacuum the cedar closet, making sure to vacuum any shelves off to remove remaining dust. Remove cedar dust particles from the closet floor, as well.
Pour a quarter-size amount of cedar oil onto a clean, soft cloth. Rub the oil into the surface of the cedar wood, adding more oil as needed. Buff the cedar with a clean, dry cloth so there's no excessive oil that might transfer to clothing.
Allow the cedar closet to sit empty for 24 hours so the cedar oil can soak into the wood.