Cut away the loose edges and paper along the crack. Slightly widen the crack with a utility knife. Wipe away dust and debris from the drywall surface using a damp rag.
Push the drywall in on both sides of the crack, testing whether you feel movement. If you feel movement, drill drywall screws into the drywall on each side of the crack. Make sure the screws go into the wood framing behind the drywall.
Cover the crack with a thin coat of drywall joint compound. Spread the compound with a 6-inch drywall knife. Make it smooth.
Cut a length of drywall tape long enough to fully cover the crack. Center the tape over the crack, and embed it in the wet joint compound using your hands. Place the end of a second piece of tape at the end of this first layer if the tape isn't long enough to cover the entire crack. Do not overlap the tape.
Spread a second coat of drywall joint compound over the crack to cover the tape. Smoothly feather the compound out a couple of inches beyond the tape. The tape will be slightly visible through this second layer. Follow the joint compound manufacturer's guidelines for how long to allow it to fully dry.
Apply an additional layer of joint compound over the dry patch. Completely cover the tape, and smoothly taper the compound out beyond the tape to avoid any humps. Allow the compound to dry.
Sand the spot lightly with 150-grit sandpaper, removing any ridges. Be careful not to sand down to the tape underneath.