the actual process is really simple. I use goats milk so my rendition of the process includes that. wear gloves and glasses to protect yourself when working with the lye, lye mix and raw soap.
Melt your oils till just fluid in a stainless steel bowl and set aside. don't get it hot. 110F is plenty hot.
Take your goats milk that has been previously pasteurized and frozen (I freeze it in 7 oz baggies or in ice cube trays) break it up a bit and place in a stainless steel or plastic bowl and adjust weight. Sprinkle your carefully measured lye crystals over the milk stirring constantly. The lye will melt the milk. Do this outside or in a well ventilated area. Avoid breathing the fumes. (if you want to use water you can, it doesn't need to be frozen just cool)
slowly pour your lye/milk mixture into your oils and stir with a stick blender. continue mixing with a stick blender until it "traces". (don't let your blender overheat, you may have to give it a rest occasionally) a "trace" is when the mixture leaves a visible trace on the surface when dribbled. add any fragrance you wish at this point. My first attempt I figured i would do it the old fashioned way and stir by hand. after 45 minutes it still hadn't traced. I purchased a stick blender and all have traced within 15 minutes. There are some things that modern tools are worth...to me at least.
pour into a mold. I made a wooden mold that is 1" thick and approx. 10.5"x 7" ID. this accomodates a 1lb batch of soap (referring to the oils)
Allow to set up for about 24 hours, until it is solid enough to cut into bars and turn out of the mold. let cure for about 4 weeks (or more)
you've got soap! always run your recipe through a lye calculator to make sure that everything is in the correct proportion to each other or it can be a reall mess.