there are several methods. The best option is to have an old ringer wash mashine, unfortunately they are harder and harder to come by unless you purchase some of the new fangled buggers as mentioned above.
Simple solutions to this are
couple five gallon buckets with a hole through the lid. Get a plunger and plunge wash rinse repeat...

There is a sweet video somewhere on the net, but i cant find it at the moment,,, I know lowdown knows where the video is at though maybe he will reply...
There are some cool metal plungers out and available for purchase although i find them a bit pricey for my frugal self...
This is what i do for laundry here Wash tub and a cheap four dollar plunger. Fill with water, clothes and soap of your choosing (only about half the amount of soap you would use in a machine) . I then agitate the water and clothes then i use my handy dandy industrial mop bucket with wringer to wring the dirty water. I then rinse clothes in same manner and i generally do a second rinse as well. The wringer does a pretty good job and is much easier on the hands than wringing by hand. The mop bucket and wringer serve other purposes so they are not just more junk scattered about the house.