Well it depends mostly on how picky you are on the quality of your soap. Still; in moder times it's usually a bit of concentrated leye (NaOH dissolved in water) + fat => soap + alkohol (H6C3O3).

As you will virtually always have excess leye as well as the alkohol mentioned to get rid of; the mix is heated and (very) diluted Hydrochloric acid is added. The idea is that the dissolved soap will 'sink' (right word escapes the memory...) to the bottom before the dissolved NaCl will so you can skim the alkohol and dissolved NaCl from the top...

Problem is here that if you add too much acid you will find yourself with something your neighbours are not going to approve of: Butyric ('butter') acid. Combined with the heat it needs little explanation why...