Spread plastic tarps over the floor of the room to make cleanup easier after completing the repair. Position a ladder under the cracked area of ceiling and put on safety glasses.
Climb the ladder and place the tip of a putty knife almost perpendicular to the ceiling and rub it gently over the crack to loosen any debris along the edges.
Open a tub of joint compound and scoop up 1/2 to 1 cup of the compound using a trowel. Lift the trowel to the ceiling and hold it at a 45 degree angle. Scrape the trowel over the ceiling to apply the compound in a thick coat. Continue until the crack is completely covered.
Wait 24 hours to allow the joint compound to dry completely. Put on the safety glasses and a dust mask. Sand the surface of the joint compound with fine-grit sandpaper, such as 100, until the surface is completely smooth and even with the remainder of the ceiling.
Examine the crack to see whether it is completely covered. If needed, apply more joint compound. Allow the compound to dry overnight and sand the ceiling again.
Open a can of primer and pour it into a paint tray. Apply the primer to the ceiling using a paint roller with an extension handle.
Allow the primer to dry overnight and paint the ceiling. If the ceiling is textured, spray the repaired area with a ceiling texture spray to create the dimpled appearance.