If you happen to be cooking over a wood fire, you can learn from our ancestors and use wood ashes to clean your pots, pans, and dishes. Mixing wood ashes with fats and oils left in dirty cookware will make a very basic type of soap that works well.
People have used wood ashes as a source of lye to make soap for centuries. The small amount of lye you extract from a few cups of wood ashes will not harm you but it can leave your hands dry. Be sure to wash them after the dishes are cleaned and maybe put on some protective lotion.
Take your greasiest pot and add a few cups of wood ash to it. Add some hot water to make a paste; the hot water will create potassium salts from the wood ash that will mix with the fats in the pot to make a rudimentary soap. When the paste is cool to the touch rub it all over your dirty dishes. Then just scrub and rinse your dishes. Make sure you use purified water to clean the dishes; they’ll be touching food again and you don’t want any disease-causing organisms to come into contact.
You can also make soap to keep on hand this way. Just put a couple of cups of woodash into a bucket of water. Let sit a while. Add some animal fats to some of the water and cook till it thickens. You can also use vegetable oils like olive oil. This is called castile soap. Add oatmeal and herbs to make it nicer. Let it cool and put into jars. The last batch I made I poured into the plastic molds of Easter chocolate praying hands and crosses. They were pretty.