Widen the crack slightly with the pointed end of a church key can opener. Run the opener along the crack to scrape away the loose plaster.
Remove 1/4-inch of plaster at each end to lengthen the crack slightly so the patching material has a solid surface at each end on which to adhere. Vacuum out the crack to remove the plaster dust.
Wet the plaster inside the crack and the wall around the crack with water and a paintbrush. Spread vinyl spackling compound along the crack with a flexible-bladed putty knife. Firmly push the spackling compound into the crack, overlapping the wall on both sides of the crack.
Add another layer of spackling compound after waiting for the first layer to dry for one to two days. Smooth the wall with fine-grit sandpaper once the spackling compound dries.
Chip away any loose plaster along the edges of the hole with a stiff putty knife. Use the pointed end of a church key can opener to undercut the edge of the hole in the plaster. Scraping away a bit of plaster from the lath beneath the edge of the hole will allow the patching material to adhere to the surface. Vacuum out the hole in the wall to remove any plaster dust.
Moisten the wall around the hole and the edges of the hole with a damp sponge. Place premixed plaster patch into the hole with a stiff putty knife.
Spread the patching material with a drywall taping knife. Fill the hole with patching material until the material is about 1/4-inch below the wall surface.
Score the surface of the wet patching material in a crisscross pattern with the edge of the taping knife. Let this layer of patching material dry for about 30 minutes.
Dampen the surface of the scored material and the surrounding wall with a damp sponge. Apply enough patching material to fill the hole. Spread the material over the edges of the hole and smooth it onto the surrounding wall. Allow the patching material to set overnight.
Apply vinyl spackling compound over the patched hole with the taping knife. Extend the compound evenly over the wall about 1 inch beyond the edge of the hole.
Sand the patch with fine-grit sandpaper after allowing it to dry for three or four days.