Remove loose drywall pieces and dust from the hole. Cut loose wallpaper away from the damaged area.
Apply spackling paste to the hole using a plastic putty knife. Press the spackling paste into the hole and draw the putty knife across the hole. Make sure you completely fill the hole with paste. Allow the paste to dry completely.
Sand the repaired area with fine-grit sandpaper or sanding block. Make sure the surface is level with the rest of the wall and smooth to the touch. Wipe away sanding dust with a micro-fiber cloth.
Prime the repaired area of wall with interior wall primer. Be careful not to get primer on the adjacent wallpaper. Allow the primer to dry completely.
Cut a piece of wallpaper to patch the repaired area. Make sure you allow for pattern matching when selecting the piece of wallpaper. Hold the piece in place on the wall to ensure you've gotten the exact cut needed.
Apply wallpaper paste to the back of the patch piece of wallpaper and carefully position the wallpaper on the repaired area. Smooth the wallpaper piece into place with your hand and use a seam-roller around all the edges.