Attach a hose or brush to the vacuum cleaner. Remove cushions and other items from the futon and vacuum the mattress, sides and back of the futon furniture to remove loose pet hair.
Remove remaining dog hair with a lint brush by brushing the futon in a downward motion. Pet stores carry specialized lint brushes, but you can also use duct or masking tape.
Soak a sponge in water. Remove the excess water so that it remains just damp. Blot the futon with the sponge to remove loose pet hairs. Rinse the sponge when it becomes full of hairs and always wring out the excess water.
Remove the futon mattress cover if possible. Launder the cover according to manufacturer directions. Washing the futon mattress cover works best for futons covered completely in pet hair.