Move as much furniture out of the room where you will be installing the outlet as possible. Cover any that remain with plastic sheeting for protection.
Locate an electrical outlet set in the wall near where you want to put the outlet in the tile floor. This is where you will tie in the electrical wire for the floor outlet. Use construction crayon to mark the outlet.
Mark a spot on the tile floor where you wish to put the new outlet with the construction crayon.
Lay out the path for the electrical conduit from the outlet on the wall to the outlet on the floor by marking it with the construction crayon. You want the shortest distance between the two outlets but, at the same time, you'll want the path to pass underneath a continuous straight line of tiles.
Mark off the row of tiles to cut with duct tape on either side to protect the neighboring tiles. Cut through the grout on all sides of each tile along the row with a rotary cutting tool and stone cutting blade.
Use a prybar to wedge each tile up from the row. Take care not to damage the surrounding tiles as you work. Gently wedge the pry bar underneath the tile, tapping it with a hammer as needed to drive it under the tile until it pops out of the grout.
Purchase or rent an electric jack hammer from your nearest hardware store. These construction tools aren't as bulky as hydraulic jackhammers and are suitable for residential construction needs. Put on the proper safety equipment and carve out a shallow trench, about 2 inches wide by 2 inches deep, for the electric conduit from the wall outlet to the floor outlet location. At the floor outlet location, carve out a hole big enough to hold the outlet box. Clean up the debris with a shop vac and broom.
Turn off the electricity for the wall outlet at the main circuit breaker. Test the outlet with a voltometer after the power has been cut to ensure that the line is dead. Remove the outlet cover and pull the socket from the wall outlet box.
Remove the floor moulding directly beneath the outlet box with a hammer and chisel.
Continue drilling out the conduit channel with the jackhammer a few inches past the moulding so that it ends directly beneath the wall outlet.
Loosen the retaining screws on the wall outlet and pull it from the wall.
Fit together an "L" shaped piece of plastic conduit so that it leads down from the outlet box and projects outward at the bottom of the "L." Test by fitting the outlet into the wall. The bottom part of the "L" should rest comfortably in the channel.
Measure out a length of electrical cable long enough to reach from the wall outlet to the floor outlet with about a foot or so to spare. Trim off the white and black wire covers with wire strippers. Slowly push this through the bottom of the "L" up until it emerges inside the outlet box. Wrap the black wire around the terminal marked "Hot" on the free side of the outlet and the white wire around the terminal marked "Neutral" opposite the "Hot" wire. Connect the bare copper wire to the green screw inside the box.
Measure and cut conduit to reach from the bottom of the "L" to the floor outlet box location. Cut the conduit with snippers or a hacksaw. Sand down any rough edges with sandpaper. Push the free end of the cable through the conduit. Apply primer to the end of the conduit and then glue. Gently press the end of the conduit into the "L".
Pull the other end of the wire into the outlet box. Secure the outlet box to the conduit with primer and glue.
Restore power to the electrical circuit. Check that the wire is live with the voltmeter. Check your wiring at the wall outlet if it is not. Turn off power to the circuit.
Cover the outlet box with plastic. Fill in the conduit channel and area around the outlet box with concrete. Allow the concrete to dry per manufacturer's instructions.
Replace the moulding and any pieces of drywall that you knocked out beneath the wall outlet.
Apply adhesive grout to the floor along the tile path and lay down replacement tiles. Grout the spaces between the tiles after the adhesive has cured.
Connect an electrical outlet to the wires in the floor outlet box in the same manner as the wall outlet box. Secure the socket in the floor outlet box with the included screws.