Common sense rules apply...
1. To wash clothes properly requires soap. Doesn't have to be washing powder, or any fancy soap, but you need to shift dirt, sweat, oil and odour, and preferably leave a slightly perfumed scent in place. Hot or warm water washes better than cold, but cold is better than nothing. If you don't have a wash-tub of any kind available, squidge everything around in a plastic bag. Any old plastic bag, so long as it's not full of holes, and it weighs nowt and can be disposed of afterwards. Rinse out all the soap afterwards.
2. Wet stuff dries quicker if you get rid of as much water as possible first. Wring out clothes. Whirl them around. Slap them against a rock. Basically get rid of water by any means at your disposal. If you have a towel, roll your wrung, whirled and slapped stuff inside the towel, roll it tight, and jump up and down on it. You'll end up with a wet towel, but at least you don't have to wear the towel the next day.
3. Never let the sun go down on your washing. If you finish a day's walk in stinky clothes, and the sun is shining, then washing clothes takes priority over pitching the tent, eating and drinking. Things dry best on sunny days, but the sun is on its way down, so every second counts. A sunny spot with a breeze is best of all, so scout around to find one.
4. Have some strong, light cord at the ready and get a line, or lines, stretched out in the sunny, breezy spot. Hang the clothes in such a way that the maximum area of fabric is exposed to the sun, and catching the breeze. If you have a handful of tiny clothes pegs, this is a doddle, but if not, then accept it's just going to take longer, because it's likely that your clothes are going to be folded double over the line.
5. Keep returning to the clothes and keep re-arranging them, so that damp patches are continually turned towards the sun and breeze. If you find that water has migrated to hems, or to the toe-ends of socks, give them another thorough squeeze, or they won't dry properly.
6. No sun... no breeze... pouring with rain? Not necessarily a problem. If you can get indoors you can still make a pretty good stab at getting things dry... but arrange wet clothes where they'll get the maximum airflow, and keep re-arranging them. Last resort, if you're camping in the rain, is to get clothes as dry as possible by as many methods as possible from above, then wear them. Might not feel pleasant, but might not take long to dry either.
7. Give yourself a fighting chance. Polyester and nylon will dry quicker than cotton or wool. In the worst conditions, cotton won't dry at all. Soggy footwear responds best when stuffed with cumpled newspaper, so don't ever pass a discarded newspaper late in the day, if your footwear needs drying!
It might read like a horrendously complicated list, but the main thing is for it to become a ROUTINE, so that you hardly notice it, and let it merge in with all the other things you do after a day's walk. Clothes can be drying while you are doing other things... just as you can do other things while you're waiting for a pan of water to boil.
