It's really easy if you have non-sheet vinyl AND a replacement tile. You simple remove the damaged tile and glue a new one in place.
If you have sheet vinyl, you still need a good 'scrap' piece but it's a bit trickier. Here's a professional's WEB link for making repairs. Repairs. If you're not comfortable with it, contact the mfgr for instructions. If you don't know whose floor it is, perhaps the previous owners do. (Maybe a neighbor has their number since they tend to keep in touch w/each other.)