Washing clothes is (un)fortunately part of everyday life in most current societies. It is as important as staying fresh while travelling! In the same "clean idea", you can have a look at the free shower article.
It will depend of course, on the different types of fabric you took with you! Anyway, try to have some inner layers (that touch directly your body) that dry fast. If you wash a t-shirt, one pair of socks and one underpant everyday, it should take you less than 15min. Consider using biodegradable/natural soaps, especially if your traveling style brings you to wash in nature.
- Shower wash is a nice technique if you travel with two or three underwears only. Whenever you take a shower, you wash socks and underpants directly (even t-shirt can be done). You can travel with a small brush as well.
- Sink wash: Fill the sink with water and block it, some people travel with a sink stopper, but a piece of cloth can make a pretty good job already. Add some soap, squeeze, move, impregnate your clothes with the soapy water. You can use a brush and/or rub the fabric against itself. Take the water out, and re-fill he sink with clean water to rince once or twice your stuff.
A nice touch is to wash and rince first your cleaner stuff like t-shirt instead of dirtying the water at the beginning with socks and underwear.
- Waterproof bag wash: The same as above, but you use these waterproof bags, usually to protect electronics, passports and so one. You put directly water with soap and the stuff you want to wash. Then you close it, and you squeeze the bag, you move it a bit like a washing machine would do. You can leave it staying like this some time, and open it as well and give a mix with your hands. Then rince with your favorite technique!
First, squeeze them as much as you can. You can twist the fabric to get more water out, but it damages the clothes. If you or the hostel have a towel, then lay your towel on the ground and lay one piece of cloth on it. Roll the towel with the cloth and then squeeze, press, sit, walk or even jump if you feel like it on the rolled towel. The water will be soaked by the towel and your stuff will dry much faster.
Hang it in a ventilated place, open window/door is better, if possible next to air conditioner or fan, or hanging above the radiator. On some radiatiors, it is unadvised to just put it in direct contact, as your clothes can take fire, even if it is more unlikely to happen. Consider having a rope with you to hang all this beautiful mess, and it has some multiple uses!
- Oh no they are still wet!! No problem, if they are just a bit wet and that it is not freezing outside, just wear them and they will be dry in a sec'.
- The non-ecological way: Use an iron/hairdryer of the hostel or host!
- I don't want to wear wet clothes but I don't want to destroy the environment: If you blow on it for long enough with a lot of motivation, you might have some results. A bit more difficult technique would be to hang them at your backpack while walking. The good thing about this technique is that you can show the world how cool your underpanties are.
The other options
In some countries, laundromats or more often laundy services are so cheap that you might prefer spending the time chilling in the sun more than rubbing the stains out of your cherished pair of jeans. The hostel you are in might have a laundry service, usually cheaper than a laundromat. Another good option is counting on the kindness of your hosts he he.
Otherwise just wear dirty clothes or buy some new ones, it is maybe the easiest way.