Locate the seam (or crack) in the drywall on your ceiling. If taping paper has come away from the seam, simply pull away what you can. Then sand the area to ensure that no other taping paper is loose. If drywall is loose around the seam, use a tradesman's knife to scrape away all loose drywall. Apply mesh tape (sticky on one side) over the seam so that the center of the tape covers the seam. Press the mesh tape against the seam with your hands to make sure it is stuck firmly to the drywall.
Place some joint compound in a drywall tray. Apply the compound to the seam with a six-inch drywall knife: smooth the compound over the mesh tape from one side to the other, continuing in like fashion down the length of the mesh tape. Finally run the knife from one end of the mesh tape down to the other, to flatten out the compound.
Wait for the compound to dry. Sand the area so that the new compound is smooth. If a second layer of compound is needed (if part of the mesh tape is still visible), apply again and sand when dry. Apply primer and paint to tie the area in with the surrounding color scheme(s).