Unplug the wire from any electrical source. Check the wires, and ensure that there are no exposed copper ends sticking out. If the plastic outer covering is only frayed or torn and nothing more, you can proceed to tape the wire.
Look at the entire length of the wire, and determine how many places need to be taped. If enough of the wire is frayed or ripped, cover the entire length.
Measure the wire. Cut enough tape to wrap around the wire. You will have to wrap the wire twice, but only cut one piece of tape at a time. If the wire is longer than 6 inches, cut the tape into sections.
Start at the end that is away from the electrical connector. Start wrapping the tape around the wire in a clockwise motion. As you finish each segment, smooth out the tape with your hands. Continue to do this for the length of the wire. When you get to the end where the plug for the current is, wrap the tape around twice, but do not allow the tape to overlap onto the plug.
Cut any excess tape from the wire. Look closely for any exposed areas. If you missed anything, just tape over the area. Plug the wire back once you are sure nothing is exposed.