I dropped a baseball cap in a puddle of mud. I'm afraid to drop it in the laundry. How can I best clean it?
If you afraid that just putting it in the washing machine can damage your cap or just don't have a washing machine, you can fill your washing bowl with hot water and add some soap or... shampoo :) Scrub your cap with some brush.
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After washing, remove the soap from your cap with water and dry it with a towel or with a fan (it is more effective). If you don't have a fan, you can put some paper in the cap - it will absorb the water.
The cap has no oil stain, which is good. I recommend power washing with a hose. Because fabric on the bill of the cap is not flexible, the dirt cannot be worked out, and rubbing the bill of the cap may set the dirt. Power washing with hot water will flush the dirt out. Add soap and rinse the soap through the stiff parts of the cap, then rinse again to get the remainder of soap out. If there is no oil or grease component, all should come out.
The first thing to do is not wet it - let it dry out completely, take a stiff brush (something like a vegetable washing brush or a stiff nail brush), go outside with the cap and scrub at the mud till you've got most of it off. Provided its only mud, most will come off - my cap's black, so that's all I need to do, although if it still looks a bit 'grey', I rub it over with a damp cloth afterwards. If yours isn't black, you may then need to do something 'wet' as suggested in another answer.
Put it in the top rack of the dishwasher. You can rubber band the bill around a suitable glass or bowl to retian its shape. In fact, they even sell plastic molds for hats specifically for this.