By Gene and
Step 1 : Prepare the work area and expose the corner bead
Lay down a drop cloth to protect the floor beneath the damaged corner and carefully remove pieces of the loose drywall. You'll expose a horizontal piece of metal called corner bead that was used to trim the corner and form a junction point for the pieces of drywall. If the corner bead is dented, it is easier to cut out the damage rather than trying to straighten the dent.
Use a hacksaw to cut through the corner bead above and below the damaged area. Then remove any drywall nails or screws holding it in place. Put the claw of the pry bar under the nail head and gently remove the nail. To remove a drywall screw, tap a Philips head screwdriver into the recess in the drywall screw's head and remove the hardened joint compound. The back it out with the screwdriver.
If the corner bead is not dented, leave it in place. Use the crevice tool of a shop vacuum to remove all the loose drywall and compound surrounding the damaged area.
Step 2 : Install new corner bead
Drywall corner bead comes in 8-foot sections but sometimes you can purchase a shorter piece from a lumberyard or home center. Cut a section of drywall corner to replace the section you cut out. Loosely fasten one side of the corner bead with a few drywall nails, align the center of the corner with the existing corner bead and when you're sure it is straight, drive the nail tight. Then use a nail set to drive the nails flush with the surface of the wall.
Step 3 : Apply joint compound
Apply a first coat of joint compound with a putty knife flaring the compound where it meets the surface of the wall. Fill and smooth one side of the corner with the compound and let it dry. Then do the other side.
When dry, sand and apply a second coat to both sides of the corner wall. When dry, finish sand the surfaces so they conform to the wall surfaces.