Our first solution was a washboard, remember them?? It actually worked well, or so my better half advised me.
Now we tend to head for the sun so clothing usually involves shorts T shirts and swimsuits, so washing can be done by hand a lot of the time. For bedding etc then we use the camp machine, if available or laudertette.
My wife's advice is to do it regulalry and not let a big pile build up, as that can be depressing. Also if you have kids, get them to join in. We found they had fun and as it is hot and sunny, who cares if soap gets everuwhere.
As the 'boss' I controlled operations froma chair with a cold beer.