With a utility knife, cut a piece of wallpaper a few inches larger than the damaged section.
Place it over the damaged section and hold it in place with blue 'safety' masking tape, being sure to match the pattern.
Use a sharp razor blade to trace the area to be removed, cutting right through both pieces of wallpaper at the same time. Try to make your cuts follow the pattern as best you can. (If possible, align your repairs along a seam.)
Carefully remove the top piece of paper and set it aside.
Use the razor to lightly score the wallpaper to be removed and apply water to loosen the adhesive (see 'eHow to Remove Wallpaper').
Use a putty knife to remove what you can't lift off with your fingers.
Clean or sand the area underneath the paper until it's smooth; use spackling compound to fill any dents. Apply primer (sizing) if you're down to a raw surface on the wall.
Apply wall-covering adhesive to the new wallpaper and place it on the wall.
Wipe away any adhesive on the surface with a damp sponge, then use a seam roller (see 'eHow to Hang Wallpaper') to press down the edges of the patch. Wipe the paper clean again.