Protect your eyes and skin by wearing protective goggles and gloves.
Weigh out the water in a medium sized bowl.
Weigh the lye in a small bowl.
In a well ventilated area, carefully pour the lye into the bowl of water. Do not do this the other way around, meaning DON'T pour the water into the bowl of lye.
Carefully stir the lye and water until the lye has fully dissolved. It will begin cloudy, and it will get hot, but as you leave it to rest for several minutes, it will begin to clear up and cool down.
Meanwhile, weigh the olive oil in a large bowl.
Carefully pour the lye solution into the bowl with the olive oil.
Mix gently at first to incorporate the lye mixture into the oil.
Once combined, you can begin to blend the mixture with an immersion blender. This process will take several minutes.
As you blend the soap mixture, you will notice that it begins to get thicker and more opaque. It will eventually thicken up into a consistency like a salad dressing. This point is called "trace." If you've made soap before, you'll notice that it takes a bit longer for this soap to reach trace than soaps with some other oils. It also is a bit thinner than many other soaps when it reaches trace. You can pour it into molds a trace, but it will take a bit longer to thicken up.
Once you have reached trace, you can add in your fragrance oils. My favorite is lavender essential oil. Not only do I love its scent, but it tends to be longer lasting than some of the other essential oils when used in soaps.
Pour the soap mixture into your mold(s). You can use silicone pans or molds, lined wood or cardboard boxes, or even plastic Tupperware type containers as molds if you don't have a mold specifically made for soap.
Set the soap aside and allow it to rest for several days. Pure Castile soap will take longer to harden than most other soaps. I think I unmolded mine (the one in the video) two days after having made it, but it was still very soft, almost like butter. I could have (should have) waited longer, but I wanted the mold for another soap. :) In any case, while soft, you can fix some of the surface imperfections by smoothing it with a knife (like I show in the video).
Wait longer for the soap to harden a little more before cutting the soap into bars (if you've used a large pan type mold). In the video, I think I had waited another 3-4 days. You'll notice that the soap had a lot more solid consistency and was already lighter in color.
Your soap is now finished, but will need to be left to dry out and cure for at least a month. This is a soap that really benefits from a long cure time. Some people even wait a year before using their pure Castile soap!
Notes
When I finished making my pure Castile soap, it looked a lot like butter. In fact, a friend came over and saw it sitting on my kitchen counter the day after I unmolded it and asked, "So you're making butter now?"
With time, it has gotten a lot harder and a lot whiter. I was actually quite surprised as to how white this soap turned out considering that I had made it with a pretty dark colored extra virgin olive oil.