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 always-hot wire from the receptacle is spliced to the black wire on the fixture cable, and to a pigtail that connects back to the hot terminal on the receptacle. At the light fixture box, the black is spliced to the black from the switch cable. At the switch box the black wire is connected to the bottom terminal on the new switch.
These sockets have two terminals, one for the hot wire and one for the neutral. A third contact may be present but is not used for this circuit. This diagram illustrates wiring for a standard, one setting lamp. This socket has two terminals, the brass for hot and the silver for the neutral wire.
This diagram is similar to the one above, but the switch comes before the new light in the circuit. New cable is run from the receptacle to the new switch location and from there to the light location. The switch may also be added in the the same box with the receptacle as in the diagrams at this link, where the two are installed in a double-gang electrical box.