Remove any loose drywall material from the damaged area using a putty knife as a scraper. Use a utility knife to cut off damaged bits of drywall that won't remove by scraping.
Sand the area using a drywall sanding screen. This removes any rough areas and helps the repair to bond more securely.
Lay self-adhesive drywall tape over the damaged area. Ensure that the entire area is covered with the tape even if you have to lay pieces of tape parallel to each other. Fold the tape in half length-wise and put it in the corner.
Smooth joint compound over the tape using a 6-inch drywall knife. Hold the knife at a low angle to the surface to spread the joint compound and at more of an angle to remove excess material. Drag the edge of the knife along the joint formed by the wall and the ceiling to spread the joint compound into the corner. Make the joint compound as smooth as you can, then let it dry for 24 hours.
Rub a drywall sanding screen lightly over the repaired area to smooth out any high areas of joint compound. Apply a second coat of joint compound if there are any low or missed areas. Let the second coat dry for 24 hours and sand it.
Paint the area with touch-up paint that matches the rest of the wall. Use a paint brush to apply the paint and feather it into the area around the repair.