For the process of saponification to occur, all the ingerdients must be in liquid form (this includes all of the oils, fats and the alkali). For this reason, we use water in the soap formulation to dilute the alkali, and the oils or fats (those that are solid at room temperature) should first be molten before the process can begin.
The alkalis used for soap making are Sodium Hydroxide (chemical formula: NaOH), and Potassium Hydroxide (chemical formula: KOH). Both NaOH and KOH are solids (pearl / flake and sometimes powder) when supplied in their concentrated form. When chemists talk of "alkali", they generally refer to Sodium or Potassium Hydroxide. When we talk of "caustic soda", we usually refer to the same thing - whereas a "caustic solution" or "lye solution" is the strongly alkaline liquid made by dissolving either pure NaOH or KOH in water. Soap has distinct properties dependant upon the nature of the alkali used in their production, Sodium Hydroxide (NaOH) gives "hard soap" . Whereas, when Potassium Hydroxide (KOH) is used, a "soft soap" is formed.
The process of making soap is called saponification. It is the chemical reaction between a fat (acid) and the NaOH (base) to produce a salt (soap) as per illustration below