Ok, Here is the method I used.
A) Soaked the hatY ) ***s) in warm water. about 30 minutes just long enough to throughly soak the hat. The soap permeates the fabric easier.
B) I used Era liquid dish washing soap and a "used" toothbrush. I was told to use a dish washing soap to break up the oil in the sweatband. I scrubed with the brush to remove the dirt and grime. I did the seams, inside and outside the sweatband. I don't think you can use to much. I let the hat soak over night in a sink full of water.
C) I washed them in the Clothes washing machine on delicate cycle with no laundry soap.
D) I hung them up to air dry.
They look great. I had been relegating them to doing household chores when they got dirty and buying new.