Mark the length of the wall on both sides of the corner with a pencil and a tape measure. Make the marks 2 inches in from the corner.
Draw a line to connect the marks, using a straight edge and pencil.
Cut out the plaster along the lines to the corner, using a utility knife. Score the plaster along the line and then methodically slash at the plaster with the knife until it is all gone.
Cut two strips of drywall 2 inches wide and the length of a standard piece of drywall, using a tape measure and straight edge.
Screw the pieces of drywall to the wall at the corner. Ensure that the drywall does not overlap the corner. Use 1-inch drywall screws and an electric drill with a driver bit installed to fasten the drywall strips.
Fit a metal corner bead over the corner and secure it in place with half-inch drywall nails and a hammer. Ensure that the corner bead fits tightly against the corner.
Smooth joint compound over the wall and to the edge of the corner, using a 6-inch drywall knife. Cover the metal corner bead completely with joint compound. Make the joint compound as smooth as possible with the knife. Allow the joint compound to dry 24 hours.
Sand the repaired area with a sanding sponge. Use the sanding sponge to sharpen the corner, but be careful not to sand off too much joint compound and expose the corner bead.