Washing machine. Use woolite or similar "gentle" detergent and LOTS and LOTS of fabric softener. Put the washer on gentle, short cycle, small load, cold water. Rinse the dirt out of the chaps before putting them in the wash, to get most of the dirt out. Lay flat to dry on a dark towel, not in direct sunlight.
Just don't do this very often, lol. Use a stiff horse brush to knock off dried mud as often as possible.