Turn off the electricity that runs to the chandelier by shutting off the appropriate breaker in the main service panel of your house.
Remove the collar that hides the connection between the chandelier and the ceiling. Collar styles vary, but it is probably held on by small screws that either screw it to the shaft or press against it and hold it in place.
Remove any screws that are holding the chandelier to the ceiling, while at least one helper supports the chandelier's weight. Lower the chandelier enough to gain access to the wires in the electrical box. Remove the nuts that attach the wires of the light to the household electric wires. There will probably be a black (live) wire, a white (neutral) wire and a bare (ground) wire. After you have separated the wires, carefully lower the chandelier to the floor.
Remove any shades and light bulbs from the chandelier. Unscrew the light sockets and disconnect them from the wires. You now have a chandelier with bare wires protruding from the main entry point at the top of the chandelier and from each of the locations for the lights. Because chandeliers are made in many different sizes and styles, you will need to adapt instructions to your particular circumstances.
Draw the new wire through the body of the chandelier by hooking it to the end of the old wire and pulling the old wire out the other end. The old wire will pull the new wire through the hollow brass tubes of the chandelier. If you have a chandelier that can be disassembled, you can do this job in sections and then reassemble the chandelier.
Attach the light sockets to the new wires, then pull excess wire back through the main point of the chandelier where it meets the ceiling. Don't pull too hard on the wires.
Reinstall the light bulbs and shades. Lift the chandelier back up the ceiling and connect the ends of the new wires to the wires in the electrical box. Reattach the chandelier to the ceiling and replace the collar.