Cut a piece of leftover wallpaper slightly larger than the torn area on the wall, using a utility knife. Place the new wallpaper on top of the damaged area on the wall. Try to match the damaged area’s pattern scheme. Trace out the shape with a pencil, then cut through both layers of wallpaper at once with the utility knife.
Remove the new wallpaper portion and set it aside. Wet a sponge with warm water and wipe the damaged wallpaper. Let it soak to weaken the adhesive backing.
Lift the damaged wallpaper section. Use a putty knife to lightly score the areas you cannot remove with your hands, being careful not to damage the drywall underneath.
Run your palm on the drywall underneath the removed wallpaper. If it is rough, sand it with 80-grit sandpaper until smooth. Fill spackling compound into any dents in the drywall. Let the compound dry.
Put wallpaper adhesive on the back of the new wallpaper portion and then press firmly onto the wall. Clean any excess adhesive on the wall with a damp sponge. Use coloring materials or markers to mend the gaps as needed.
Mix dishwashing detergent and warm water to make a cleaning solution. Gently rub the spot, using a sponge with the solution. Increase the ratio of the detergent if your first attempt wiping off is not successful. Dishwashing detergents contain degreaser that helps remove grease spots and stains.
Apply white vinegar or rubbing alcohol and wipe with a sponge. Be careful not to soak the area as it will affect the adhesive on the backing paper. Rub the spot dry with a cloth. Repeat this step until you get all the stain off the wallpaper.
Apply commercial wallpaper cleaner if all else fails, following the manufacturer's instructions.
Clean dirt off the wallpaper with a damp sponge dipped in distilled water and let dry. Scrap off any loose plaster with a razor blade and then apply a coat of oil primer seal to coat these areas.
Apply a thin coat of drywall plaster to fill the holes, if any, from the scraped plaster. To smooth the scraped surface, add a second coat of oil primer seal to restore these areas.
Touch up the smaller damaged wallpaper areas with watercolor paint, using a spotter paintbrush. Dilute the paint in water for the first layer. Increase the opaqueness of the subsequent layers until the colors match the wallpaper's. Fix large sections with a bigger paintbrush, using the same method.
Clean the wallpaper periodically with your vacuum cleaner's wall brush extension tool. If you do not have this tool, wipe with a dry, clean cloth.