Use your hands or a screwdriver to pull away any loose drywall or debris from inside the crack. This will provide a solid base for your repair work.
Mix a joint compound (spackle) with water according to the manufacturer's instructions. Use a putty knife to fill the crack completely full of the spackle, then wipe away any excess material with your knife.
Place a piece of fiberglass mesh tape over the patched area, then apply a thin layer of spackle over the top, using your putty knife.
Wait 4 to 6 hours for the spackle to dry before proceeding.
Use a medium-grit sandpaper to hand-sand the patched area, including the tape and the spackle. Sand the patched area until it is smooth and level with the rest of the ceiling.
Paint the patched area using a bit of touch-up paint to complete the project.