Mark, I soak the face fibres first then turn it over to soak the back.
Clean and rinse as needed.
Turn it face fibre up and then soak again.
Then clean and rinse untill it rinses clean water.
If its really soiled then I would turn it over and over again cleaning and rinsing each time.
Best, Dave.
P.S. Last pictures, this is the silk one Pete was refering too.
This is a rug that needs to be continually brushed, either as it is drying which is best but certainly after it has dried. See my last post about drying rooms, this is definately when I needed one.
The pictures are from opposite directions for obvious reasons, its still wet and will look much better when dried and groomed.