There's the old fashioned method of beating the clothes with rocks down by the riverbank...
We travelled overseas on the cheap and found no washing facilities anywhere, so we used the bathtub and threw the kids in on top to do the "grape stomp". We had a small clothes rack which we put on a sunny balcony for drying.
Other things I've seen - there was a small portable washer I remember seeing, it was like a canister which you screwed down (a bit like a large thermos flask) and then you turned the whole thing with a handle. Apparently this agitated the wash and also built up pressure inside, which forced the dirt out of the clothing. Although it was so small they showed how you could wash two double sheets in there in one go. It had a rubber gasket to stop it leaking, you had to open it carefully because of the bit of pressure, but it seemed to do a good job. I think it might have been made by Husqvarna, I'm not sure.
And another I've see, courtesy of Nimbin (Australia's answer to Woodstock) - in the hippy commune for alternative lifestyle people, one bloke invented a pedal-powered washing machine using a discarded exercise bike and a plastic garbage bin. He hooked the bike up to the bin so that as he pedalled, the bin got shaken around. He would undo the bin lid, put in the clothes, some water and some washing powder, then clamp the lid back on and pedal. That way he said he got exercise as well as clean clothes!
I hope that helps.
Marg