Place a stepladder underneath the ceiling crack. Step up and brush the crack with a soft-bristle brush to knock off any crumbling bits of plaster or drywall. Wipe down the area around the crack to remove any dust or dirt (dust clings even to ceilings) with a damp rag. Allow the area around the crack to dry before applying any caulk.
Insert a tube of painter's caulk into your caulking gun, push the plunger down to the base of the caulking tube, and release the trigger spring. Cut off the tip of the tube nozzle at a 45-degree angle and at a point where the width of the nozzle will match the average width of the crack.
Step back up onto the ladder. Fill the crack with caulk using steady, even pressure from the trigger and slowly drawing the nozzle of the tube down the crack.
Draw a putty knife gently across the crack to smooth the caulk out and remove excess caulk. Allow the caulk to harden.