Spread a drop cloth under where you'll be working. Position a ladder or stepladder in a spot that gives you easy access to the crack.
Cut a narrow groove into the crack in the drywall with a utility knife. Brush out any debris in the crack. Push up and down on either side of the crack and you'll probably feel a slight "give" in the Sheetrock. This needs to be corrected or the Sheetrock will crack again.
Pound drywall nails into the Sheetrock on either side of the crack, making sure that the nails sink into the wood behind the Sheetrock. Use a drywall hammer to ensure that the nails are properly countersunk into the Sheetrock.
Place a piece of drywall tape over the crack and the nails. Spread drywall joint compound over the paper with a 10-inch taping knife. Make several passes over the compound, working outward to feather the edges.
Sand the joint compound after it has dried to ensure a smooth surface. Wipe off any drywall dust with a damp rag.
Paint the repaired area to match the surrounding ceiling.