Unplug the LG unit if it is currently plugged in.
Remove the LG from the wall, if this is a wall mounted unit. This can usually be done by lifting up on the unit to free it from the mounts and then pulling it forward.
Set the LG unit on a stable surface such as a floor or worktable.
Remove the cover for the unit. The screws for most LG air conditioners can be found on the back of the air conditioner. Loosen these with a screwdriver before removing the cover. Depending on the model, you may need to first pull off any knobs before removing the cover.
Follow the electrical cord to where it connects to the terminals inside. Look for the brown and black wires screwed into the terminals on the main PCB assembly.
Make a note of which wire is connected to which terminal. Unscrew the terminals holding the brown and black wires in place. Pull the wires off the terminals with needle nose pliers.
Strip off 1/2 an inch from the end of the brown and black wires from a replacement cord.
Connect the replacement brown and black wires to the terminals. Squeeze the ends of the wires around the terminals with a pair of needle nose pliers. Tighten the terminals.
Replace the LG air conditioner cover and secure. Rehang the unit on the wall, if needed. Plug the air conditioner in and test.