Locate an interior electrical outlet that corresponds with the location on the outside wall where you'd like to install the exterior outlet. Turn the power to the circuit off at the home's circuit breaker panel.
Remove the cover plate for the interior outlet. Take out the screws at the top and bottom of the existing outlet and pull it out of the box. Loosen the screws on the side of the outlet and set the outlet aside. Loosen the screws holding the outlet box to the wall stud and pull the box out of the wall.
Drill a 3/4-inch hole through the exterior wall from the inside out, using an impact drill with a carbide tip bit.
Place a weather-proof exterior outlet box on the exterior wall, lining up the hole in the wall with the opening in the back of the box. Mark the location of the box's mounting screw holes onto the wall with a pencil. Drill shallow 1/8-inch holes into the wall at the marked location. Line up the box with the holes and attach it to the wall with masonry screws.
Slide a length of 14-2 electrical cable into the hole in the wall from the outside. Pull it out the opening inside the home. Feed the cable into the opening on the rear of the outlet box you removed earlier. Remount the outlet box.
Remove three inches of insulation from the end of the cable inside the house with wire strippers. Remove 1/2 inch of insulation from the black and white wires inside the cable. Wrap the bare wire ends of the old cable around the lower screws on the side of the outlet and the new cable wire ends around the upper screws on the side of the outlet. Match white to silver and black to brass. Tighten the screws.
Place the in-home outlet back into the outlet box and attach with its screws.
Trim the cable end at the exterior end in the same fashion you employed earlier inside. Attach the wire ends to the new outlet and install the outlet in the box. Place a weather-tight cover onto the exterior box.