Use a 6-inch drywall knife to scrape off all the existing plaster from the damaged seam. Pull off the existing tape, exposing the seam completely. Scrape off any residual plaster. Expose and clean up the whole seam, even if only part of the seam has damage.
Press mesh adhesive tape over the seam, covering the entire length of it. Press the tape to the ceiling with the palm of your hand to ensure that it's flat.
Spread joint compound over the tape from one end to the other, using the 6-inch drywall knife. The line of compound should be slightly wider than the tape, so it covers the tape completely. Ensure that the surface of the compound is flat and smooth.
Allow the compound to set for five or six hours. Use the drywall knife to scrape off any ridges or peaks.
Apply a second coat of joint compound on the seam using your 12-inch knife. Make the seam an inch or two wider on both edges than it was. Let it dry for five or six hours. Scrape off any ridges.
Apply a third layer of joint compound, making it a little wider still along both sides. Let it dry overnight.
Sand the seam with a drywall sanding pad to get it flat and smooth. Repaint the ceiling.