There are actually two different kinds of homemade soaps that soapmakers like to make. One of them is called 'Cold-Process' soap and the other one is a glycerin soap. Cold process soap takes a lot more work for the average soap maker, but the results are worth it. Cold process soap starts out with heating oils, and mixing lye with rainwater. I know that sounds harsh, but there is a chemical process that takes place in which the lye actually isn't lye anymore by the time the product is finished. Something happens when the lye water combines with the oils, and a process called saponification takes place. After the soap mixture is poured into the molds, it begins the process of 'curing'. It takes about three weeks before the soap is fully cured and is safe to use. During the curing process, the lye water with the oils forms what we know as soap. If done properly, the soap will work as soap and the product is amazing to use.
Glycerin soaps, on the other hand, are made by soap makers who take small pieces of glycerin (usually the glycerin is in a big bar, usually 5 LB or 25 LB. Pieces are taken off and put into a pot and heated at a low temperature. When it is melted, coloring and scents are added and the mixture is placed in a mold. If the glycerin bar is transparent, items can be placed inside the melted glycerin and it makes it more appealing, especially for kids. This method is usually called 'Melt and Pour' or 'M and P'. There are soap making lists that you can join on the internet, and there are companies that specialize in soap making and sell soap making products.
So that is the basic story of how homemade soaps are made. Contact me if you are interested in watching me make homemade soap, and I will try to arrange a time when I will be making soap and you can watch.