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.