Adapters, like the one pictured, are available from hardware/home stores to make this type of installation. One of these may be required for light fixtures missing the necessary parts to fit the electrical box. For high ceilings, the threaded rod length can be adjusted to suit most situations.
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.
Run the new cable from the source electrical box, through the notches and into the new outlet box. Pull an extra 8-10 inches of cable into each outlet box to allow for stripping and connecting the wires.
Decide on the location for the new electrical fixture and where the source will be. Determine inside of which walls and ceilings the cable must be run. For example, with a new ceiling fixture using a source from an existing wall receptacle, the cable will have to be run inside the wall cavity, through the top plate, into the ceiling cavity, and on to the new fixture.
After the installation is complete, cover the notch with a metal shield, available in the electrical section of home stores. Repair the wall over the shield and the hole in the ceiling to finish.
Try to remove the wallboard cleanly so it can be reattached when you’re done. The baseboard can be reinstalled without replacing the wallboard, but this will create easy access for pest such as rodents, as well as drafts from cold air during the winter.
Use a straight edge held flat against the top of the base cap to keep your line straight as you pull the knife through the caulk several times until it’s cut cleanly.
Mark each stud for notching using one of the nail guards as a template. Use a handsaw to cut the top and bottom lines for the notch to the depth of the plate thickness.