Slide on a pair of work gloves and safety glasses to protect your skin and eyes. Drill a 1-inch hole, using a masonry or wood bit, through the wall of the room that holds your current power box, 6-inches above the flooring surface.
Insert a piece of 1-inch PVC piping through the hole, so a minimum of 1-inch of piping extends from both sides of the wall. Attach a 90-degree PVC elbow fitting to the exterior side of the pipe. Adjust the fitting so the 90-degree turn is aimed downward.
Bond the fitting and pipe together using exterior-grade silicone caulk. Attach and bond an elbow fitting -- aimed upward -- on the interior side of the pipe for the subsequent running of wire.
Dig a 24-inch-deep trench from the current structure -- your house, for example -- to the unattached garage using a shovel or trench digger. Fit a 1-inch-wide piece of PVC piping into the trench.
Measure the length from the bottom end of the exterior PVC elbow down to the entrenched pipe. Subtract 6 to 8 inches to allow for an additionally PVC elbow fitting. Cut a piece of PVC pipe to the adjusted length using a hacksaw.
Fit the cut pipe into the bottom end of the PVC elbow. Fit and bond the bottom end of the cut pipe to the entrenched pipe using a third PVC elbow.
Drill a hole in the wall of the garage 6 inches above the surface of the floor. Insert a piece of PVC piping through the hole, so a minimum of 1 inch is exposed on both the interior and exterior sides. Fit and bond the exterior side of the piping with a fourth PVC elbow.
Measure the length from the bottom end of the fourth exterior PVC elbow down to the entrenched pipe. Subtract 6 to 8 inches to allow for an additional elbow. Cut a piece of PVC pipe to the adjusted length using a hacksaw.
Fit the cut pipe into the bottom end of the fourth PVC elbow. Attach the bottom end of the cut pipe to the entrenched pipe using a fifth elbow. Cover the entrenched pipe with dirt.
Attach and bond a sixth and final PVC elbow to the interior side of the garage pipe. Cut a hole in the garage wall 36 inches above the surface of the floor, to dimensions of your outlet, using a drywall saw.
Run 12-gauge UF cable through the PVC piping from the house to the garage. UF cable is coated in plastic sheathing and is suited for most interior and exterior home electricity installations.
Strip 6 inches of sheathing off the garage-end of the wire. Cut off the plastic coating of the three individual copper wires within the sheathing.
Attach the copper end of the red (hot) wire around the positive extension on a ground fault interrupter (GFI) outlet. Attach the white (neutral) wire around the negative extension on the GFI outlet. Attach the green (ground) wire to the ground screw on the back of the GFI.
Screw the outlet into the wall using a drill and 3/8-inch screws.