Begin by using a utility knife to trim away any frayed edges or overhanging wallpaper. You may be able to push some of the raised edges back into the opening to conceal them. Make certain that no edges will result in raised surfaces on the finished repair.
Apply the compound across the taped area, spreading it thin and smoothing it using a joint knife or a putty knife. Make certain that you apply enough compound to fill the void behind the tape, then work off the excess with the drywall knife. When patching over nail holes, dimple the area by striking it with a hammer (this will provide a better surface for holding the drywall compound). Once compound has dried, sand it smooth and repeat the process with another layer of joint compound, if necessary.
Sand, prime and paint the patched area.