An isolated-ground receptacle makes use of an extra wire for a separate ground in the circuit. This is the red wire in the 14/3 cable used here which is marked and connected to the grounding terminal on the receptacle. The other cable wires are connected as with any other circuit except for the ground wire. The bare copper ground wire is NOT connected to the receptacle, instead it is connected to the grounding terminal inside the electrical box where the receptacle is housed.
New 2-wire cable is run from the receptacle to the new light fixture. At the receptacle the wires are removed and each one is spliced to the new cable and back to the receptacle with a pigtail splice. At the light fixture box the black wire connects to the hot terminal, the white connects to the neutral terminal and the ground to any metal grounding terminal on the fixture, outlet box, or both.
This diagram shows the wiring for a new receptacle added from a light switch. The switch must have an always-hot wire for the source and a neutral wire must be present for the return path. The hot source is spliced with a pigtail back to the switch, and to a new 2-wire cable running to the new outlet. The neutral is spliced in the switch box to both the existing light, and the cable to the new receptacle.
At the switch, the other end of the black wire is connected to the bottom terminal on the switch and the black wire going to the new light is connected to the top terminal. The white wire from the receptacle is spliced to the white wire going to the light, it doesn’t connect to the switch in this diagram, but a new electronic switch will usually include a neutral wire connection. At the light the black wire connects to the hot terminal on the fixture and the white goes to the neutral terminal.