I'm honestly not sure that there is one. Water will over time, wreck the suede, a very slightly moisted cloth will take the top layer of dirt off but it won't actually clean them. You can get regular shoe cleaner for them which actually lasts quite some time. That's exactly why I went to using leather half chaps. Found it was just easier to get all leather than leather and suede.
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.