Cut a groove along each side of the crack using a utility knife.
Clean out the crack with a putty knife to remove any scraps of drywall. Vacuum the crack.
Drive a nail into the stud behind the crack using a hammer. Use a stud finder if there is not a stud directly behind the crack. Most reappearing cracks appear near a stud location. Locate the closest piece of wood possible. Place a nail every few inches up the right side of the crack. Add nails to the left side, staggering the nails just below the ones on the right.
Cover the crack and the nails with drywall mesh tape.
Apply joint compound with a broad putty knife. Feather the drywall compound out so that it is thinner moving away from the crack. Allow the compound to dry. Sand down the compound the next day. Vacuum away the dust and make another application. Repeat this a total of three times.
Paint the putty area with a paint primer. Allow the primer to dry. Paint the patched area the original color.