Sometimes you have to patch holes in drywall. Either there is a dent in the wall, or you had to cut an access hole. The fix, fortunately, is simple enough.
Wooded slates and drywall
When you cut a hole to install wires, do not throw away the piece of drywall you just cut out. It perfectly fits into the hole. It can be used to cover the hole back. To provide a surface to mount the drywall to, secure two thin pieces of wood along the edges of the drywall with screws. Put the piece of drywall in place and secure it to the slats with screws. The hole is covered.
Apply join compound along the gap. Cover the gap with joint tap. If you skip this step hairline cracks could appear along the joint. Cover the tap with compound. Feather out the edges. Sand the first coat after it dries. Apply a second and third. Sand between coats. Apply a finish and paint.
This technique is economical and efficient. Since the drywall piece is flush with the rest of the wall, the patch is easy to cover. Other than speed there is no reason to use any other technique.
Metal Plate method
The home centers sell thin metal plates to cover smaller holes. Stick the plate over the hole with the adhesive side down. Cover it with joint compound. The compound will dry in the little holes in the metal plate. This creates a surface like drywall. Sand the first coat, and apply a second. Sand again. If you can feel imperfections with your hand, especially at the edges, apply a third coat. If required, apply a texture. You are ready for paint.
The metal plate can be perfectly blended into the surrounding wall. It will not be visible on the finished surface. The plate, however, is not load bearing. You cannot install a wall hanger right on top of the plate. This is still possible when using the other technique.