Cut out a rectangular patch that is a few inches larger than the damaged area. You can use a piece of wallcovering that was left over when it was initially installed. If you don't have a part, find a place where you can "steal" a patch, like behind the refrigerator, inside a cabinet, or behind a mirror.
Determine how the original paper was applied. If it was pre-glued to the back, you will need to moisten the back of the patch with a sponge to activate the adhesive; otherwise, cover the back of the patch with a thin layer of wallpaper paste.
Making sure your patch lines up precisely with the pattern on the installed wallcovering (Image 1), press the patch firmly into place (Image 2) and allow three to five minutes for it to stick.
Once the paste has had a chance to set in, use a utility knife with a new blade and ruler to cut a rectangle around the inside of the patched area (Image 1). Cut straight lines to form a neat cutout and avoid cutting corners too much. Once you've made your cuts, remove the portion of excess wallcovering that surrounds the newly cut area.
Then very carefully remove the freshly made patch from the center (Image 2).
Use the knife to pull up the freshly cut corners of the damaged piece that was under the patch, and carefully lift and remove the damaged section.
Making sure the patterns match, firmly press the new patch into place and smooth it out with the wallpaper sponge. Since the new patch and the old damaged section were cut together, the patch must match the cutout area exactly.