"Erase" the scuff mark with a pencil eraser.
Try to scrape the scuff off with your fingernail.
Buff away the remaining scuff with a felt cloth.
Apply vinyl floor cleaner to a sponge or mix a concentrated cleaner according to the manufacturer's instructions. Scrub the scuff with the nonabrasive side of the sponge. Rinse the sponge thoroughly.
Saturate a corner of the sponge with rubbing alcohol. Hold the saturated part of the sponge on the scuff mark for a few moments to allow the alcohol to penetrate. Rub the scuff forcefully. Rinse the sponge thoroughly.
Apply scouring powder to the sponge. Work the powder over the scuff with increasing pressure until it's apparent that the powder isn't working.
Rub the scuff with fine steel wool, beginning with light pressure and working up, until any remaining scuff mark is gone.
Apply floor wax to the scrubbed section of flooring if scrubbing removed the vinyl's finish. Follow the manufacturer's instructions.