Remove any furniture coverings that can be removed to wash or dry clean. When washing, add 1 cup of white vinegar to the wash water, and dry with mild heat and a clean filter.
Roll the surface of the furniture with a lint roller, or pat with a length of broad sticky tape, such as packing tape, duct tape or masking tape. As the sticky surface fills up with fur and dandruff, replace with a clean section of tape, and continue until nothing more sticks to the tape.
Wipe down the furniture with a slightly damp, thick, soft sponge. Rinse the sponge out frequently in clean water and squeeze until it is nearly dry. Fur and dandruff will adhere to the surface.
Put on latex or rubber gloves and dip gloved hands in clear water. Shake off drops of water and rub over furniture surfaces with your gloved hands, working into crevices and places that were overlooked by the tape and sponge treatments. As you go, rinse gloved hands in clear water to remove fur and dandruff.
Vacuum carefully, using a vacuum with a clean HEPA filter, to ensure collection of the last of the dandruff.