I figure I'd do a write-up. It's dead simple and with this method you don't have to crawl under the car.
On the Vulcan and Essex, the P/S reservoir is on the engine and it's big enough for a turkey baster. I had a real cheap turkey baster that fell apart after a few pumps and left fluid everywhere so it got messy.
On the Duratec, my turkey baster wouldn't fit so one day I was washing my hands and thought "Hmm, that thing will work" so I saved the soap bottle once it was empty. You'll also need trans fluid. Doesn't matter what trans fluid. I had some leftover Mercon and thought I'd use it all up. I'll need to pick up some full-synthetic for later. Not pictured is a bottle to catch the old fluid.
So, just take the pump off the soap bottle and make sure you rinse it good before using it! Don't want to contaminate the P/S system with soap. And then just start pumping into a bottle. I used an old water bottle. It's easier to use two hands.
I managed to pump about half a pint out of the reservoir. The P/S system is about a quart.
This needs to be done once a week for about a month so clean fluid is gradually put into the system to clean it and then siphoned out and replaced. Eventually it'll all be clean.
Note: the soap pump might not work on the Essex or Vulcan because the soap pump isn't long enough. Use a turkey baster for those engines. Go buy one. Your mom/wife/girlfriend won't appreciate you using her turkey baster.