How can I rewire this circuit?
This is how I suspect the circuit is wired, but you'll have to investigate to be sure.



In the fixture junction box:
White = Grounded (neutral) conductor.
Black = Ungrounded (hot) conductor.
Red = Switched ungrounded (hot) conductor.

The circuit may be wired this way because it continues on to feed other rooms, or simply because the switch is a "smart" switch that requires a grounded (neutral) conductor.  

You'll learn a bit more about the circuit, when you open up the switch box and take a look inside. If you're still not sure what's going on, you'll have to probe the wires to gain a better understanding.  If at any point you don't feel comfortable, or you're in over your head. Don't hesitate to contact a local license Electrician.