Taking care of a hakama is pretty simple. Jun makes it way too hard. Find a washer, throw some detergent in, follow it with the hakama and whatever else needs washing. Take your best guess as to a good temperature. I've tried many variations, all seem to work pretty well. When it's done, find a dryer and throw the hakama in along with whatever else needs drying.
The above works, of course. However, I've heard that if you try that (using a washer and dryer) with a 100% cotton hakama from Bu Jin (like one of my hakama), you'll end up with one of those "stone washed" hakama. Admittedly, some people like them, but I prefer the traditional look myself...