Use your putty knife or scraper to tear up a corner of a strip of the vinyl wallpaper. Grasp the corner firmly between your thumb and middle finger and give it a good tug. If the vinyl is thick, you may find that the wallpaper tears off easily in large sheets and leaves just a little bit of wallpaper paste behind. If this is the case, count your lucky stars, then soak a rag in some wallpaper stripper to loosen the remaining paste. Gently slide the softened paste off with your putty knife or scraper.
If your vinyl wallpaper isn't very thick, you'll first have to tear the vinyl layer off the wallpaper. Loosen a corner with your putty knife or scraper, then tear as much of the vinyl off as you can. Soak a rag in some wallpaper stripper and sponge it onto the remaining wallpaper. As it softens, scrape it off gently with your putty knife or scraper. You may have to repeat the procedure on any remaining wallpaper paste left on the wall underneath.
Rent a wallpaper steamer or purchase an inexpensive garment steamer. The second option may be the least expensive, and you'll wind up with a steamer that you own. Start by peeling the vinyl layer off the wallpaper. Then fill the steamer with water, according to the manufacturer's instructions. Start steaming the wallpaper in small sections, scraping off the softened residue with your putty knife or scraper. By using the steaming method, there shouldn't be any paste left on the wall after the wallpaper has been removed.