Turn off any electricity that is running to the hanging lamp you are going to be rewiring. This is extremely important, and must be done before you begin this project.
Locate the following parts of your hanging lamp: the outlet box, which is flush against the ceiling, the cross bar and screws that connect the outlet box to the ceiling, and the two wire nuts that actually supply the electricity to your lamp.
Remove the base of your hanging lamp, so you can just work with the outlet box and the wire nuts. Remember to keep track of all of your lamps parts and screws, so you are able hang it back up once you finish rewiring.
Take off the cross bar by taking out its screws. This will allow you access to the wire nuts.
Connect your new pig tail wires using the wire nuts. Make sure that the pig tail wires and the wires coming from the outlet box are the same color when you connect them.
Replace the cross bar with the screws you removed before, and hang your lamp back up on the ceiling. Turn the electricity back on and flip the switch. As long as your lamp lights up, you have successfully rewired your hanging lamp.