Put on safety goggles and gloves before working with lye. This is just a safety precaution because lye is caustic and can burn your skin.
Weigh out the lye and water in glass, ceramic, or heavy plastic bowls.
Add the lye to the bowl of water (and not the other way around!) in a fully ventilated area. (I usually do this step outside.)
Mix together well the lye and water until the lye has fully dissolved. You will notice that it heats up and gets more opaque first and then it will cool down and get clearer. Leave the mixture to sit in an area where it won't be disturbed by anybody or any animals.
Weigh out all of the main oils (olive oil, coconut oil, neem oil, rapeseed oil, and castor oil- not the essential oils) on a kitchen scale. I find it easier to tare a large bowl and then add each oil to it, taring again between additions.
Add the lye solution to the oil solution and gently mix together.
Continue mixing the ingredients with an immersion blender until you reach trace. Trace is the point of making soap when the saponification process has begun. It is when the mixture gets more opaque and thicker, looking like an emulsified sauce.
At trace, you can now add essential oils. You can either weight them out and add them, or add some and take a whiff to see how strong the fragrance is.
Fully incorporate the essential oils into the soap mixture.
Pour the mixture into molds. I like to use silicone loaf pans, but you can also use milk cartons, plastic containers, or, of course, soap molds. :)
Cover and insulate the soap with a towel, and set it aside where it can stay undisturbed for a day or two to harden up.
Check on the soap occasionally, and unfold it when it appears hard enough to easily unfold without breaking.
Cut the soap into bars. For this particular use, I like to make big, chunky bars of soap that are easy to hold onto when washing our dog. They've worked really well for us so far!
I stamped a paw pattern into my soap, while it was still somewhat soft, using the plastic caps of items I found around the house. You can decorate your soap with soap stamps or rubber stamps or something else like I did at this point.
Set the soap aside for a few weeks to dry and harden up more. While the saponification process will have completed within a couple of days and you can technically use it then, the soap will harden and improve with drying time, meaning it will also last you longer when using it.
You are now ready to give your dog a bath! Have fun, and try not to get too wet! :)