Hi, Joe. At the home centers you can buy strips of aromatic cedar about 1/8" thick in packages especially for lining closets. Have an idea how many square feet you will need before you go and don't forget to get at least 10% more than your calculated footage. The packages have instructions for installation.
One thing I might mention. When I go to the lumber yard that has all their cedar in one barn, I enjoy picking out the boards. The guys that work there hate going in the building. Regular cedar has the same smell as aromatic cedar, just not as strong but since there is a lot of wood the smell is strong. I'm not around the smell often so it is kind of neat to me. The guys that work in the building are around it all the time and get very, very tired of the same smell. Based on this, I would not build a cedar closet directly off a bedroom or in any other part of the house that was used regularly. And I would be sure that the door to the closet closed tightly. I think that you want to try to limit the smell to the one closet. Just a suggestion.