Scrape the damaged drywall tape off the seam with a 6-inch drywall knife, pulling up the plaster that's over it as well. Get the seam between the two sheets of drywall completely exposed.
Press mesh drywall tape along the seam, covering it completely. Press it firmly to the surface. Cut it with a razor knife at the end to fit.
Cover the whole seam with joint compound, from end to end, using your 6-inch drywall knife. Smooth and flatten the compound so it completely covers the tape.
Allow the compound sit for six hours. Scrape it with your drywall knife to knock off any ridges or high spots.
Spread on a second layer of compound, this time using a 10-inch drywall knife and making the seam of compound about 1 inch wider on either side. Get it smooth. Let it dry.
Scrape over the second to knock off any ridges or high points. Apply a third layer, making it wider still. Smooth it out and let it set.
Sand the final layer smooth with a drywall sanding pad. It's now ready for painting.