Brush away any bits of loose or crumbling drywall from the gouge.
Score the drywall with a utility knife about 1 inch around the outside edge of the gouge and peel away the protective drywall paper covering inside the scored line.
Apply only enough drywall compound to the gouge, with a 6-inch taping knife, to fill it completely. Smooth the blade over the wall, removing any excess drywall compound from the surface of the wall.
Sand the gouged spot with a drywall-sanding screen after the compound dries completely. You can use a drywall-sanding pad, but if the gouge is small, you can wrap a sanding screen around a block and use that to sand over the spot.
Apply another coat of wet compound to the spot, smoothing it as you did the first time. You may notice that the first coat of dried compound shrunk a bit, leaving a slight depression.
Sand the spot again when dry and use your fingers and a strong light to check for any imperfections. If the gouge is large, you may have to apply three or four coats of drywall compound before it dries flush with the surface of the wall.