I've seen a lot of filthy thru-hikers over the past week and would like to share some know-how for staying clean on the trail, especially in the hot, arid sections.
Where trail grime comes from
Abundant desert dust sticks to any moisture it encounters. If you are sweating, dust will accumulate where there is sweat. The coarser the weave of your clothing, the more dust will collect there as well, if the clothing is moist. Dust does not tend to settle on dry objects, so, the best way to avoid grime is to be dry.
Most hikers are wearing long pants and long-sleave shirts. Many or most of these hikers already have dark swaths of grime under their shoulder straps and in other places on the clothing. The weave of this clothing is usually coarse to allow for maximum breathability, and a lot of dust settles in the fabric. Of course, these items are not washed on a regular basis, and hand washing is rarely sufficient to clean them. So, they grow dirtier and dirtier and soon stink up, especially if the fabric is synthetic. Even if you sponge yourself down at night, every morning you put the same filthy clothes back on. Only a laundromat can clean these clothes now, and so there is more reason to go into town and spend hours there, getting a hotel room for convenience.
My alternative is to avoid these problems by keeping as dry as possible by wearing fewer clothes and carrying a sun umbrella. Sometimes it is too windy for brief periods to use the umbrella, but at this point my skin is tanned enough to go without the umbrella for up to half an hour if I need to. I wear airy polyester running shorts whose weave is too tight to accumulate dust, and on top I wear a merino wool T-shirt that I take off if I start getting too sweaty. Sometimes I get a little damp on my lower back where my back touches my pack, but that's about it. When it's colder, I put a fine-weave windshirt on over the T-shirt. This way, I avoid the grime problems that are already beginning to plague many thru-hikers.
As a rule, it is much easier to wash dust off one's skin than to get the grime out of dirty clothing. My legs can be quickly cleaned at night by passing a wet sponge over the skin. My shorts don't often need cleaning and can simply be rinsed in water. Same with the windshirt. The T-shirt can use a washing about once a week. The only items that need frequent, serious washing are socks and underwear. These can be washed using the ziploc bag trick -- put some water and some soap (Dr. Bronners or shampoo) in a ziploc bag with the items and agitate them, then repeat the process in a bag of clean water with no soap for rinsing.
To wash my body with little water, what I usually do is put some water in a cup, add a few drops of Dr. Bronner's liquid soap, and wash and scrub myself with a small sponge. There is just enough soap to make me feel cleaner, but not so much that I would need to rinse myself off afterwards. Hair washing requires more soap (shampoo) and is usually done separately and not as often.