While it's true that grandma used mothballs in her closets, these days health concerns make it desirable to find less toxic ways to repel moths.
Use dried lavender in sachets. Place several in the closet. Lavender oil also works. Soak cotton balls in the oil, then put them into a cup and leave cup in closet or drawer. Lavender is a good moth repellent and will keep your clothes smelling fresh.
Use dried mint leaves, another moth repellent. Put them into a cloth bag or sachet and place among clothes or hang in the closet.
Use a piece of cedar wood or cedar chips to keep moths at bay. Or, buy sheets of cedar wood and line closets and drawers with them. As the scent fades, sand a cedar piece to keep the odor and oils at the surface.