The longer you travel, the more likely you'll need to wash your clothes. You can:
Use a laundromat (if available) - common in Europe, but not so common in Asia and South America
Use the hotel's laundry service
Pay some locals to wash them for you
Wash them yourself - e.g. in the hotel bathroom
Hand washing
The cheapest way to do your laundry (albeit not the most thorough) is to do it yourself.
In the bathroom, fill the sink or bathtub with water, some sort of soap (or shampoo, body wash, laundry detergent), and your dirty clothes. You can use a universal sink stopper or just a dirty sock.
Let it soak for about 15 minutes
Swish the clothes around. Scrub each item individually by rubbing the cloth together, concentrating on areas such as the armpits and stains. Apply additional soap as needed.
Rinse each item under a faucet (e.g. the shower) until the water runs out clean, not soapy.
Wring the excess water out of the item.
Hang up your clothes: outside is best or use a portable clothes line. Try to let them dry as long as possible, e.g. overnight. You can also try using a hairdryer, if available.
If you_fre clothes are still wet, pack them in a separate, plastic bag.