take a toothbrush and scrub the sweaty parts of the hat with some shampoo, then wash the hat. most hats will keep their shape just fine in the washer and dryer.....or air dry. shampoo is made to break down body oils. you can also use this tip for ring-around-the-collar.
You can also stop sweat stains before they happen. I use a product called Hat Saver that you spray on the outside of your new hat and you never get sweat stains to clean. I then just wash the headband on the inside of the hat if it starts to smell or gets real dirty. You can buy it at hatsaver.com.
In addition to sprays and washing, you can also protect your hat with a wicking hat liner, like the CrownWear Head Liner. The keep sweat out of your eyes and filter out the dirt, salt and oils in your sweat to prevent stains and odors and extend the life of your hat. (available at www.CrownWear.com)