Before washing dishes, I wash my hands well. I make the washing chore easier by not cooking food that gets the pot too dirty. This means no oils or grease. I'm vegan, so that makes it easier.

I use a two cup pot for all my cooking. I have a separate pot for heating water for coffee while I'm eating. I put some water in the pot and clean it with my fingers. If you don't want to use your fingers, a small square of yellow camp towel works well. I dump the water away from water sources and away from the camping spot. Usually, I dump the water in the fire.

One thing I don't do is wash the pot in a stream.

A related issue is washing clothes. If I'm on a trip where I plan to wash clothes, I bring a large plastic coffee can to wash them in. The coffee can is also hand for getting water to put out the fire.
_________________________
http://48statehike.blogspot.com/