The source neutral wire on the receptacle is removed and spliced to the white running to the switch, and to a pigtail back to the receptacle neutral. At the switch, the neutral wire is needed to power some dimmer switches and is now required in most switch boxes.
The neutral wire in this circuit is taken from the receptacle and spliced to the white on the new cable, and to a pigtail that runs back to the receptacle. The hot is spliced to the black cable wire and a pigtail back to hot on the receptacle.
This diagram illustrates some of the most common circuits found in a typical 200 amp circuit breaker box. The breakers are installed in a service panel so that contact is made with one of two hot bus bars that run down the middle of the box. The hot wire for a circuit is connected to the breaker by a set screw on the base.
This page contains diagrams to add a new electrical outlet to an existing circuit. Arrangements are included to use an existing receptacle circuit or lights and switch circuits as the source for a new wall outlet.