Scrape away all loose plaster from the edges of the crack so only solid plaster is left.
Use a hammer and trim nails to re-secure any exposed lath that's loose.
Coat the inside of the crack with a thin layer of joint compound, using a putty knife. Make the layer of compound about 1/4-inch thick.
Tear a piece of drywall tape to roughly the shape and size of the inside of the crack. Press it to the compound inside the crack. Let is set for four to six hours.
Apply a second thin coat of joint compound over the top of the tape inside the crack. Let it dry four to six hours. Repeat, adding layers of compound inside the crack until you've built it out to the level of the wall surface (usually three or four coats).
Spread the last coat of compound over the whole surface around the crack, using a 10-inch drywall knife and covering the area completely. Let it set for eight hours. Sand it smooth with a drywall sander. Repaint the wall.