Remove the damaged stucco using a hammer and cold chisel.
Examine the wall underneath the stucco. If the stucco was applied over steel mesh, inspect the mesh for damage.
Cut away the damaged mesh with wire cutters. Cut a new piece to fit the gap, and fasten it to the wall with galvanized nails. If the underlying wall is damaged, conduct repairs as necessary.
Mix a batch of stucco patching compound, following the manufacturer's directions. Apply the compound by spreading it over the damaged area with a masonry trowel. Even the stucco to the level of the surrounding wall by dragging a piece of scrap lumber, such as a 2-by-4, across the face of the wall.
Texture the stucco patch with the trowel or a bristle brush to match the texture of the surrounding stucco as necessary.