Measure out the lye and the distilled water using a kitchen scale. Wear gloves and eye protection when working with lye and lye solutions. It's best to use glass or plastic bowls for this step. (I prefer glass.)
Carefully add the lye to the water in a well-ventilated area. Do NOT add the water to the lye! Adding water to a container of lye can cause it to expand quickly, making a dangerous chemical "explosion".
Stir the lye into the water until it is well dissolved. It will be cloudy at first and will start to get hot. The mixture will later clear up and cool off. Leave it in an area where it cannot be disturbed by other people or animals while you measure out your oil.
Weigh out the coconut oil in a large bowl. It's easiest to make this soap if you melt the oil first before continuing.
Carefully add the lye solution to the coconut oil. The residual heat of the lye solution will help melt the coconut oil if you are using it solid (If you choose to do it that way, I'd recommend blending the coconut oil with a blender before adding the lye solution. Also, keep in mind that it will take longer for the soap to reach trace when using a cold oil.) Incorporate all of the lye solution into the oil gently with a spoon.
Use an immersion blender to fully mix the oil with the lye solution and help bring the mixture to trace. Trace is the point of the soap making process in which the mixture becomes more opaque and resembles a light sauce or mayonnaise. It is also the point at which the soap has begun to saponify (aka. turn into soap). In this recipe, the mixture will likely be thick from the beginning, especially if your oil was solid, to begin with. That is because coconut oil is one of the "solid oils" that can change its consistency when first reacted with the lye, making a thicker mixture that looks like it is at trace, even when it isn't (sometimes called false trace). My tip is, especially if you are new to soap making, to blend for a couple of minutes, even if it looks like it's starting to thicken, just to make sure you are really at trace before pouring your mixture into molds.
If you plan on adding any essential oils for fragrance, now, at trace, is the time to add them. I love using lavender essential oil for laundry and general cleaning.
When making coconut oil soap, the soap will harden and set up very quickly! Have your molds ready, and pour the thickened mixture into the molds. (Silicone molds don't normally need any sort of mold releasing agent. I don't normally use one for plastic either, but it's a good idea to use one when working with wooden molds or molds with delicate details. You can also line wooden molds with wax paper instead.)
Allow the soap to harden, undisturbed, for several hours. The last time I made mine in the afternoon, it was already hard enough to unmold before bedtime! That is unusual for most soaps, but because coconut oil makes such a hard bar of soap, it solidifies more quickly than most soap recipes.
Unmold the soap when it is hard enough to hold its shape. This is also the best time to cut into bars. If you wait too long this soap will get very hard and brittle and will be difficult to cut later on. (In fact, you'll see that because I waited until the next afternoon to unmold and cut mine, waiting for good lighting for taking pictures, that my soap was so hard and brittle that some of it broke into pieces when I cut it.)
If you plan on grating it, now is a good time to grate it too. You can also pulverize it in a food processor when it gets harder.
The saponification process with fully complete in the next couple of days. It's best to leave bars of soap out to dry and complete the process. With most soaps, it's best to wait to use them until several weeks (or a month) have passed. That not only allows for the saponification process to complete, ensuring that no unreacted lye is left to irritate your skin, but it also allows for the soap to harden. A hard soap will last longer than a soft bar of soap. Since this soap will be used for general cleaning, it isn't as important to wait to use it. This bar of soap gets very hard very quickly, and for laundry use can be used immediately. (You can use gloves to prevent skin irritation if you are concerned about unreacted lye.) That said, all soaps are said to improve a bit with time. This is because their crystalline structure continues to develop with time. So, use it immediately, if you like, but know that the soap should improve over the next few weeks! :)