Cut out a rectangular patch that's a few inches bigger than the damaged area. You can use a piece of wall covering that was left over from when the covering was initially installed. If you don't have a piece, look for a place where you can "steal" a patch -- such as behind the refrigerator, inside a closet or behind a mirror.
Once the paste has had a chance to set up, use a utility knife with a new blade and a straightedge to cut a rectangle around the inside of the patched area (Image 1). Cut straight lines to form a neat cutout and avoid overcutting the corners. Once you've made your cuts, remove the portion of excess wallcovering surrounding the newly-cut area.
Then, very carefully pull off the newly-made patch from the middle (Image 2).
Making certain that the patterns match up, press the new patch firmly into place and smooth it over with the wallpaper sponge. Since the new patch and the old damaged section were cut out together, the patch should match the cut out area exactly.