Measure the length and width of the crack.
Cut a piece of spare drywall to fit those measurements.
Fit the drywall into the space. If the crack extends to the corner bead -- the plastic or metal form inside the wall that helps give the arch a professional-looking shape -- screw the edge of the drywall to the corner bead with a short drywall screw. Tighten it until it is just slightly below the drywall surface.
Cut a length of fiberglass tape to cover the repair. Fiberglass mesh tape has a light adhesive back so that it will stick to the drywall. Smooth the tape over the repair.
Scoop out some joint compound with the tip of the drywall taping knife. Smooth a thin layer of joint compound over the drywall tape, feathering it out at the edges. Add more if necessary to cover the tape, but spread it out thinly. Two or three thin coats will create a more professional finish than one thick coat.
Allow the joint compound to dry for the time recommended by the manufacturer, about 24 hours. Drying time is dependent on temperature, humidity and thickness of application.
Sand the area lightly until smooth. Clean off the sanding particles with a tack cloth or a clean rag.
Apply a coat of primer to the repair and then paint it.