Thread the connector clockwise onto the twisted wires, being sure no bare copper is exposed at the bottom. Pull gently on the connector to be sure it’s secure. You can wrap electrical tape around the wires and cap for extra security or just push the splices into the back of the box and attach the cover plate.
Attach the wires to a new switch connecting the hot source to the bottom terminal and the wire running to the light to the top terminal. On a receptacle the black wire from the source goes on the hot, brass colored screws and the white goes to the neutral, silver colored screws. If there are two sets of wires on a receptacle, keep them in sets using the top terminals for one and the bottom terminals for the other set.
The best way to remove the insulation without nicking the copper is to use a wire stripper. Most strippers have a set of cutters for the most common gauges. Gently twist the strippers back and forth once or twice, and pull the insulation straight off the end.
In a room with old plaster of at least ¾inch thickness, an armored cable or greenfield can usually be run under the baseboard by chiseling a channel along the floor wide enough to bury the metal casing flush with the wall surface. The metal will protect the wires from nail punctures with this method, but care should be used when nailing baseboards to miss the cable.