Position a ladder under the crack.
Cut a V-shaped groove into the sides of the crack with a utility knife, widening it and making it easier to work drywall compound into.
Use an old paint brush do brush away any dust from the groove, then dip it in water and use it to wash the groove. Allow the area to dry.
Fill the groove with drywall compound, scraped smooth with a putty knife.
Press a piece of paper joint tape into the wet drywall compound, following the direction of the crack.
Apply more drywall compound over the tape, smoothing it against the ceiling and feathering out the edges.
Allow the drywall compound to dry for the time recommended on the container.
Sand the patch with 120-grit sandpaper and a sanding block. Resand it with 180-grit, and even 220-grit until you reach the desired level of smoothness.
Prime and paint the patch as needed to make it blend in with the ceiling.