Severe rips and punctures mean you'll have to cut out the damaged area, fix the drywall if needed and install a wallpaper patch. You'll need a piece of matching wallpaper to use as the patch. If you don't have a remnant, buy a small sample at a wallcovering store. If the pattern is no longer available, steal a piece from inside a closet or hallway.
A double-cut patch is the best way to make the repair nearly invisible. Start by taping the wallpaper patch over the damaged area with its pattern perfectly aligned with the one on the wall. If the patterns don't line up precisely, don't panic; wallpaper tends to stretch a little once it's wet and rolled out. Simply align the patterns as close as possible.
With the patch taped in place, use a razor knife and straightedge to cut through both paper layers (photo 3). Be sure to completely cut through each corner. Remove the patch and set it aside. Next, carefully peel the damaged paper section off the wall. It probably will leave behind some felt backing; you can remove this sticky fuzz with a warm, damp sponge. Then patch any divots in the wall with a nonshrinking vinyl spackling compound (photo 4).
If the wallpaper patch is prepasted paper, soak it in warm water for 30 seconds. Then "book" it by folding it over, paste to paste, to activate the adhesive. Let it set for about five minutes, then peel it apart and press the patch to the wall. Use your fingertips to adjust the patch and align the pattern (Photo 5). Smooth the area with a damp sponge, then wipe off any excess paste.
If the patch isn't prepasted or if you lifted it from another location, apply it to the wall with wallpaper paste.