You can make pure tallow soap using only tallow, water, and lye. Like in old times, some people used to make soap this way. Another way is to add other oils to the tallow soap recipe, like olive oil, palm oil, or coconut oil. Adding other oils will give your soap different properties, like more lather or moisturizing abilities.
Cold processed soap is, in simple terms, mixing oils with sodium hydroxide lye. This natural process causes a chemical reaction called saponification. Through the use of heat, fats and oils, as well as lipids, convert into soap.
Weigh tallow, coconut oil, and olive oil, and put into a crockpot on high, or a pot on the stove on low heat. Weigh the water in a heat safe container or sturdy plastic bucket, and weigh lye separately. Once oils are melted, check their temperature; you want them to be 100 degrees F.
Pour lye water into the melted tallow and blend with an electric blender or whisk by hand until you reach a light to medium trace. If you ever want add essential oils, this is the time. Stir 1-ounce (28 g) by weight of essential oil. Pour the liquid soap into a soap mold. Tap gently to remove any air bubbles.