EDIT: Oops, I only just realised that I was 4 years late.
It's made using an industrial process called saponification. Basically, an ester is boiled with sodium hydroxide (NaOH).
The common esters used are triesters, and they are usually triglycerides. They're basically made up of animal fats or any plant/animal oil.
Now there are 2 processes for saponification:
1. Kettle boiled batch process: Fats/oils are heated with NaOH to form soap. It's not a continuous process, but rather, the reactions are done in batches, hence the name.
2. Fatty acid neutralisation process: Involves a 2 stage continuous process: Production of fatty acid, then from fatty acid to form soap.
i)Hydrolysis: Fats/oils heated with water, which converts it into fatty acids
ii)Neutralisation: Fatty acids reacted with NaOH to form soaps.
Then, to precipitate the soap from the mixture, brine (concentrated NaCl solution) is added.
Then they treat the soap before packaging, ie. Soap washed, added perfume, colouring agents, etc.