Sand the drywall around the crack with medium-grit sandpaper or a sanding block. Wipe the dust off the ceiling around the crack with a damp rag.
Spread a thin coat of joint compound on the crack with a putty knife 4 to 6 inches wide. Smooth out the joint compound as much as possible with the putty knife.
Place a strip of drywall tape in the joint compound over the crack. Press the tape into the joint compound by running over it with the putty knife. Allow the joint compound to dry for the time specified on the packaging.
Sand the patch smooth with fine-grit sandpaper. Wipe off the dust with a damp rag.
Add another coat of joint compound to the ceiling over the crack, using a putty knife 10 to 12 inches wide. Spread the joint compound over an area that measures 12 to 18 inches wide to help the patch blend into the ceiling. Allow the joint compound to dry.
Sand the patch smooth again. Add another layer of joint compound with the large putty knife. Allow the joint compound to dry, then sand it again and wipe off the dust.
Apply a coat of primer to the patch and allow it to dry.
Paint the patched and primed area to match the ceiling. Apply the paint in an area about 2 feet wide to help the patch blend into the ceiling.