Scrape away any damaged or loose sheet rock along the damaged corner using a small drywall knife, exposing the corner bead.
Correct any dents or pockets in the corner bead by gently tapping them with a hammer until the corner is flat and the edge is straight and smooth.
Mix a small amount of sheet rock mud, following the manufacturer's instructions.
Apply a layer of sheet rock mud over the exposed corner bead, using a large sheet rock knife. Spread the sheet rock mud until the corner is even and level with the preexisting surface.
Let the sheet rock mud dry for one hour.
Scrape the sides of the corner using the large sheet rock knife, removing any excess drywall mud.
Add a second layer of sheet rock mud. Scrape the second coat over the first until both sides of the corner are level and straight.
Let the second layer of sheet rock mud dry for one hour.
Rub the patched corner bead with a damp rag, removing any excess sheet rock mud and blending the new patch into the existing sheet-rocked surface.