Place the furniture outside to air out, if possible. Open a window or point a box fan toward the furniture to help create air circulation if it is too large or inconvenient to move.
Spray your furniture with a pet-odor eliminator, such as "OUT!" or "PureAyre." These products work by absorbing bad smells to help neutralize the air.
Dampen a cloth with vinegar and wipe down any furniture that smells of mothballs. This works best on wooden furniture, such as tables and chairs, but can also be done on cloth furniture.
Sprinkle cloth furniture with baking soda. Allow the baking soda to sit undisturbed for 12 to 24 hours, then vacuum it.