Mike outlines the correct way to flush your power steering fluid. It can be done in about fifteen minutes and will require about three quarts of Power Steering Fluid from the auto supply.
Flush two of the quarts through the system while an assistant is turning the wheel lock to lock. Use a large drain pan underneath and lower the return line down as low as you can into the pan to prevent making a mess on the shop floor. Then hook the return line back to the pump and fill the system. It should take about a quart to refill after this operation. It wouldn't hurt to buy an extra quart.
This is not a home brew method. It is the accepted method for flushing and changing the PS fluid, and changes it all. This is actually a question on the ASE test.
Simply siphoning out and replacing the fluid in the reservoir replaces less than half the volume of the system. It's like washing your feet then putting on dirty socks.