You can literally use a (CLEAN, NEW) plunger, some shampoo (the amount you'd use on your hair is usually enough), and warm water in a large bucket (they sell them at Lowes and the like) to wash clothes in a pinch. We have done it in the past, when I was a kid we didn't get a washer until later and it was my job to do the laundry half the time starting in kindergarten. We have done this method in the past when our washer has broken too, and it works great. Wash/plunge (the plunger is the agitator), get it clean, then do the rinse the same way but with clean water. I usually had a glug (about a cup?) vinegar in the rinse water because it helps cut the soap out and keep it from frothing too much. Usually I did two rinses because I used too much soap- use less if you need to do two rinses to get it all out. You can dump all the water down the tub drain, but we also poured it in the yard or garden since it's not crazy soapy. Wring out (ball it up and step on it with your foot in the tub) and hang dry in the sun if possible.