Without Soap
1. Find sand or gravel (that from a stream or river bed is the least likely to have organic matter in it).
2. Heat water as described above.
3. Smear a small amount of any leftover cooking grease on the dishes, add wood ashes from the campfire, and mix in a few teaspoons of hot water until a thick cleaning solution results. This soapy mixture is harsh--see Warnings below.
4. Use a handful of sand or gravel as an abrasive to scrub the dishes clean, using a separate wash pot and rinse pot.
5. Drip or air dry.
6. Heat the dishes immediately before cooking with them again to help with sterilization.
Soapless Method 2
1. Before you build a campfire, clean out the firepit. Do not burn trash in the firepit. Hardwood ashes are best for doing dishes. When you are done cooking, allow the fire to burn down to a manageable level.
2. Select a good sized metal pot; if you have one that is crusty or greasy from cooking, that is the one to use.
3. Use a long handled serving spoon to put hot coals and ashes into the pot. About 2 cups will do for most messes.
4. Add just enough water to make a thin, chunky paste that is hot to the touch but not scalding, and mix it with the ashes.
5. Smear the hot ash paste liberally over all dirty dishes and utensils. It will look awful, but it works. Use the charcoal to scrub any crusted-on food. For stubborn crust, let the ash paste soak in for a few minutes.
6. Collect ample water from your source, and carry it and the dirty dishes at least 200 feet away from your water source. Nest the dishes and utensils as much as possible, and rinse them one at a time over the pile to save water. Set each rinsed piece aside in a clean, dry spot until you are done. Make sure to rinse your hands.
Warnings
* The alkali water created by mixing wood ashes with grease can be very harsh on your hands. In extreme cases, it can cause chemical burns just like an acid. Use gloves if you've got them, or a stick to do the scrubbing, and rinse your hands thoroughly when you're done.