Cleanup when you're living with family, roommates, etc. who you really don't want involved in our little bit o' fun can be difficult. Of course, it depends on how messy you're getting. If you limit yourself to, say, just your pants, socks, and assorted stuff below the waistline, a washrag, squirt bottle (or maybe two) of water, and an extra set of clothes in a gymbag or knapsack can be handy. Just remove the messy clothes, head to a laundrymat, and run everything (clothing, that is) through the cycles. The family might still have some questions, but at least you'll be relatively clean. The muddier you get, the more difficult the cleanup. An alternative naturally is scouting out puddles near creeks or other bodies of water - again, not perfect, but it'll do in a pinch.
I usually go mudding near lakes or rivers and hike in with a gallon of water, microfiber towel and small bar of soap in a backpack. You could probably even use a large CamelBak if you wanted extra 'incognito'. I either wear my mudding clothes underneath hiking clothes, or just go naked in the mud!
So, hike in, strip off hiking clothes and backpack. Go play in head-to-toe mud until I've had my fun. Do a pre-wash for body and any mud clothes in the river to get essentially all the mud off and go (still wet) to my backpack. Totally lather up with soap and use the clean water for a top-down rinse, then towel dry. Back into hiking clothes, wrap mud clothes in towel and hike out.
This will get you really clean, though as I've mentioned before, possibly even too clean. If someone gets really close, they might find you smell like fresh soap/shampoo when they were expecting a normal 'after a day of work' smell. Though you can counter that by exclaiming 'what a day, I need a shower!' as soon as you get home!
A few more little tips; if washing water is scarce I scrape off the worst with a blunt edged tool (like a ruler or similar) then use a selection of cloths, damp towels and kitchen wipes to take off the rest. Take a mirror too as it's probably the face that people will notice the most. Last of all give yourself a dousing with a large bottle of water or two.