By code the junction box must remain accessible, so look for a spot where the cover plate will blend. Use a 3x2½ inch device box like the ones use for wall outlets and set it at the same level as the existing wall receptacles to minimize visual impact.
Insert a clamp, with wires attached, into the junction box hole and from inside the box, push the included nut over the wires and onto the clamp threads. Turn the nut as far as possible onto the threads and then use a screwdriver and hammer to tap it down until it’s tight.
After choosing the electrical source, decide where to cut the walls and ceilings to run the new cable. For example, to run from an existing wall receptacle up to a new ceiling light fixture, a small hole should be cut in the corner where the wall and ceiling meet. The top plate is then notched to pass the cable and afterwards a metal plate is attached over the notch to protect the wires.
An easier alternative to repairing the damage is to use one coat of mud and then cover the rough repair with a preformed medallion. A plastic medallion can be installed using caulk to stick it to the surface or using the fixture cover plate to hold it in place. You can also get a plaster medallion, these should be installed using setting joint compound or plaster of Paris to attach it to the ceiling. Keep pressure on the medallion to hold it in place until the mud has set.