Select where you want to mount the new electrical box and outlet. Choose a spot that you can access easily from inside and outside the house. Drill a 1/4-inch hole through the wall with an 18-inch-long drill bit to mark the center of where the electrical box will be.
Insert a zip tool underneath the siding that has the pilot hole drilled through it. Run the zip tool along the vinyl siding strip to loosen it from the house. Place the exterior electrical box on the loosened siding and trace around it with a marker.
Hold the siding away from the house with one hand and use a utility knife to punch a hole through the marker tracing with the other hand. Finish cutting out the tracing with tin snips.
Bore a 1-inch hole through the wall, over the 1/4-inch pilot hole you made earlier. Turn off electricity to the power supply source. Check that the wiring from the supply source is safe to work with using a circuit tester. Run a 12-gauge cable from the power supply source through the 1-inch hole.
Use the zip tool to pull down on the loosened siding and reattach it to the siding strip below it. Remove a knockout hole from the exterior electrical box with a screwdriver and hammer. Insert a cable connector into the knockout hole and feed the cable coming from the wall through it.
Place the electrical box through the hole in the siding and against the plywood underneath. Tighten the cable connector's screw with a Phillips-head screwdriver. Drive one supplied screw through each of the screw holes.
Cut away the cable's outer casing with a utility knife. Peel the insulation away from the three wires and cut it away. Strip 1 inch of the end of each wire with a wire strippers. Bend the ends into hooks.
Loosen the GFCI outlet's screw terminals with a flat-head screwdriver. Wrap the black wire around the black, or "hot," screw terminal, the white wire around the "white" screw terminal, and the ground wire around the green screw terminal. Tighten each terminal to hold the wires in place.
Push the wires into the electrical box. Line up the GFCI outlet's screw holes with the electrical box's screw holes and use the supplied screws to secure the outlet in place. Put the electrical box's cover over the box and outlet and secure it in place with the provided screws.
Insert a tube of silicone caulk into a caulk gun and cut off the tip with a utility knife. Apply a continuous bead of caulk around the electrical box to seal the seam between the siding and the electrical box. Smooth the caulk with your finger. Restore power to the power source.