First let's cover safety.
Lye is an extremely strong base and will cause severe burns. The first step of making soap is always getting out the baking soda and keeping it close by. Use it to neutralize the lye if you get it on yourself. You should wear safety glasses if you have them available.
(Note from WW - if you don't have safety glasses, get some! As a chemist I can assure you that splash-back is a common occurrence during any kind of formulation and/or mixing. You only have one pair of eyes - the $5 it will cost your for a pair of UVEX goggles is well worth the price)
Next take all your aluminum spoons and pots and put them away. Lye will eat holes completely through them! Use glass, plastic, or cast iron pots and plastic or wood spoons.
There are only three necessary ingredients to make soap: water, fat, and lye. Soft water like rainwater works best but anything wet will work. Here on this farm we always use lard for our fat. I'm sure beef tallow or other kinds of fat would work but I've never used them. Here in the sticks all grocery stores still carry Red Devil lye; its probably in the same area of the store as the drain cleaners. If it sits on the shelf next to Drano that should tell you something. Yeah I know there are dozens of recipes out there calling for salt, sugar, borax, oatmeal, olive oil... try those after you master basic soap.
The hardest part about making soap is getting the ratio of these three right. Here is the ratio that we use: 8 oz. of fat : 3 oz. of water : 1 oz of lye.
Now here is how to make soap.
Take cold water and add your lye to it. Stir it until the lye is completely dissolved. Don't be surprised when the water boils and gets hot that's a good sign. After stirring put it over to the side and let it come back down to room temperature.
Melt the fat in a pot large enough to prevent anything boiling over or splashing out. We use a big cast iron pot outside over a fire, but that's more tradition than necessary.
Very carefully pour the lye water into the melted fat and stir and stir and stir. We use an old unpainted boat paddle to stir with but we make 20 pounds of soap at one time too. We also keep a low fire under the pot the entire time because it reduces the amount of time to stir.
When you can pull your spoon or paddle out of the pot and the soap pulls up like spaghetti with it you are finished. You can leave it in this pot and cut it out in a week or two or pour it into molds to complete the job. Finally leave the soap alone for a week or two more, the longer it has to dry out the better it will be.
Sound simple? It is but you won't need to exercise the day you do this because the stir part is a lot of hard work.