Fatty acids are carboxylic acids that contain 4-28 carbon in the molecule.
Soap is the sodium or potassium salt of fatty acid.
The general formula of soap is RCOO^–Na⁺ or RCOO^–K⁺, where R is an alkyl group that has long carbon chain.
Image below shows the general structure of a soup molecule.
Image below shows the example of a soup molecule (Sodium Stearate)

Making of Soap - Saponificationts

Alcohol react with carboxylic acid will form ester.
Example:
Ethanoic acid + ethanol → ethyl ethanoat (ester) + water
CH₃COOH + C₂H₅OH → CH₃COOC₂H₅ + H₂O
This process is call esterification, and it is a condensation reaction (take out 1 water molecule and form a covalent bond).
Inversely, the ester also can be decomposed to form alcohol and a salt by alkali such as sodium hydroxide.
Example:
ethyl ethanoat (ester) + sodium hydroxide → sodium ethanoat + ethanol
CH₃COOC₂H₅ + NaOH → CH₃COONa + C₂H₅OH
This process is a hydrolysis reaction (add 1 water molecule to the covalent bond and break the bond).

As we learnt before, salt can be produced by the reaction between acid and alkali.
Since soap is the sodium or potassium salt of fatty acid, we can produce soap by the reaction between fatty acid and alkali.
Usually, the alkali that we use is sodium hydroxide (NaOH) or potassium hydroxide (KOH).
Fat molecules are the molecules that form by a glycerol molecule and three fatty acid molecules.
Since glycerol is an alcohol, while fatty acids are carboxylic acid, the process is call esterification, and it is a condensation reaction.
Figure above shows that, we can separate the glycerol molecule from the fat molecule, and at the same time, produce three sodium salt of fatty acid.
The hydrolysis of a fat or oil is given the particular name, saponification.
The saponification reaction is the hydrolysis of fatty esters.
The saponification reaction typically refers to the reaction that is carried out by a strong base.
An example the saponification of tallow by sodium hydroxide. (tallow is the mixture of fats that are obtained by steam treating cow fat.)
Summary of saponification reaction
Normally some sodium chloride (NaCl) will be added into the solution to reduce the solubility of soap. As a result, we will obtain soap in solid form.