Suggestions on ehow to heat potassium carbonate and add water to the oxide should be politely disregarded. Also causticising is not as easy or complete as caveman chemistry implies, particularly for potassium carbonate. Fortunately for soap you don't need a pure product. There is one gotcha if you make your own lime in that you can over-burn (dead-burn? I forget where I read it) limestone, where the silicates form/melt and the product is not porous (ruined) but this should not be an issue if you use a traditional fire to make it.
About the alkali, Wagner's talks about a large inverted conical container with a tap on the base into which ash and between 1/10th and 1/12th of it's mass of lime is placed, together with enough water to slake it. That amount is not given but it will be in excess of stoichiometric. This is lixiviated until exhausted, producing three grades of soap boiler's lye. Strong, containing 18 to 20% alkali, Middling strong, containing 8 to 10% alkali and Weak lye containing 1 to 4%. The latter is usually reused in the next batch instead of water in the lixiviating stage.
The boiling of soft soap commences with a strong lye containing 8 to 10% potash, by which an emulsion if formed, the scum is dashed about with a stick, the beating-stick, and by this means all the alkali is caused to be taken up. A fresh lye is then added, and the boiling continued, until the soap stiffens on cooling to a clear tough mass. When the soap contains too much caustic alkali, which can be ascertained by the taste, more oil is added. The clear boiling now commences, during which excess of water is removed. To avoid a lengthy evaporation a concentrated lye is employed, and the soap, instead of bubbling up, has it's surface covered with blisters as large as the hand; these blisters are termed leaves. When the boiling is finished-ascertained by putting some of the soap to cool on a glass plate, from which, if firm, it can be separated-the soap is cooled and stored in barrels.
There is a lot more stuff here but it's quite broad and vague, massive amounts as the type and quality of the fat or oil. I think this is everything it says about the manufacture of soft (potassium) soap and might be as close to a pre-industrial method as I can find. Avoid aluminium containers/pans, they will be eaten, and I suggest you use an appropriate indicator instead of tasting.