Cover your pot sides and bottom with liquid soap before use. This makes the soot wipe off easily. As you fix the meal, put a pot of water on the fire/camp stove to heat. Then when you are finished, you have the warm/hot water needed for clean up. I mix the hot water in dish pans with cold water to the temp needed, one for wash and rinse. Sometimes I even use the water pan as the rinse water holder. This has worked for years. Pots and pans aren't left all black and ugly.
Source: Mom and Dad did this when we went camping.
By Trailblazer from Beavercreek, OH
This page contains the following solutions.
We love to camp and cooking over a campfire is the most fun. It's always a challenge each trip to see what wonderful meals we can come up with to cook over an open flame. But at the end of those delicious meals comes time to do the dishes.
Scrape your dishes well with a rubber spatula (scrape into a ziplock baggie or empty can), then wipe with a used paper napkin or paper towel. This gets the worst of the "ick" off before you wash.
Always take soap with you. Of course you can clean up with it, but it is also useful for protecting your pans from smoke and fire damage.
Have water heating while eating. Put on rubber gloves and add bleach to dish water and rinse water.
When I go camping, I take jugs of water, some for drinking, others for cleaning. If you have a lot of dishes, take a dishpan, add some water, pour in a bit of dish soap and do your dishes as you normally would.