It wasn't all that long ago that housewives and farmwives made a liquid soap at home using wood ashes and animal fats. The recipes and techniques have been somewhat lost through the years, but several websites have been collecting some information about the process. This website has a bit of background information on the subject, saying, "Historically, potash was derived from boiling down liquid lye (leached from hardwood ash) until it was reduced to a white solid composed primarily of Potassium Carbonate (K2CO3). Potassium Carbonate was used in soap making, glass production, and other manufacturing processes. It could be further refined in a kiln to remove impurities. The refined product was called pearl ash. Both potash and pearl ash were used as an early leavening agent in baked goods."
Farmer's Magazine (1859), estimates that ten pounds of ash will make about one pound of salts of lye. The leeched ash water is boiled "to the consistency of tar".
From Frontier Freedom Magazine and other sources, homemade lye from wood ashes produces potassium hydroxide, an alkalotic relative to the commercial sodium hydroxide that handmade soap is made with. Most online sources agree that rainwater or distilled water is the most desirable for making wood ash lye. The technique they recommend to produce lye, which also sounds to be one of the faster and safer techniques out there, requires you to fill a pillowcase with ashes and place over a five gallon bucket. Pour boiling filtered water into the pillowcase bucket, like you are making tea. Agitate for some time (1 1/2 hours?), then take the pillowcase of ashes out of the water and cook the extra moisture out of the ash water. The lye is strong enough when it can dissolve a chicken feather. The process may have to be repeated several times to get the correct strength (approximate pH?). Avoid scorching the lye (?). Liquid lye can be sun-dried/dehydrated into crystals (?).
The recipe from Frontier Freedom Magazine calls for 18.2 ounces of homemade lye crystals, 2 1/2 pints of water, and 6 pounds of fat, which they say will make 9 pounds of soap. Their single bar recipe calls for 3 heaping tablespoons of homemade lye crystals, 1/2 cup soft water, and 1 cup melted beef tallow. "A combination of half tallow and half lard is usually suggested." This is somewhat frustrating because most of us use metric measurements for everything this exacting. The soap is made via hot process, and can be hardened into bars and molded or left as a liquid for washing clothing.