Place a ladder underneath the crack in the ceiling so that you can easily reach it. Climb up on the ladder and use a paint brush to brush away all loose areas of plaster around the crack. Do not press down hard; simply wipe off any loose debris that will interfere with the patch.
Apply a thin layer of joint compound over the crack that is no more than 1/8-inch thick. Apply the compound with the flat edge of the putty knife until the crack is no longer visible.
Measure the length of the joint compound with a tape measure and cut a piece of fiberglass tape to the same length. Press the fiberglass tape up into the wet joint compound, making sure to smooth the edges of the tape down. If the crack repair area is not straight, place multiple pieces of overlapping tape along the entire area.
Scrape the entire repair gently with the flat edge of the putty knife to remove 50 percent of the joint compound that you applied before. Allow the repair to dry until it is hard to the touch.
Apply a thin, second coat of joint compound over the tape with the putty knife until the tape is no longer visible. Smooth out any lumpy areas with the putty knife.
Dampen a sponge with water and then squeeze it to remove as much moisture as possible. Dampen the joint compound slightly just until the surface appears moist. Press the flat edge of a grout float firmly against the ceiling and move it over the repair to smooth out any small lumps.
Allow the patch to dry again until it is hard to the touch and apply a third layer of joint compound, making sure not to introduce any lumps. Concentrate on feathering the edges of the repair out very thinly so that they blend in seamlessly with the surrounding ceiling.