In a well-ventilated area, put on your protective gear, including safety goggles and gloves. Carefully measure out the sodium hydroxide (lye) and distilled water in separate containers.
Slowly add the lye to the distilled water (never the other way around) while stirring gently until fully dissolved. Set this lye solution aside to cool.
Measure and weigh the olive and coconut oils accurately. If using solid coconut oil, melt it gently until it becomes liquid and then combine it with the olive oil in a heat-proof container.
Use a digital thermometer to monitor the temperatures of both the lye solution and the oils. Wait until both are around 100°F (38°C) and within ten degrees of each other.
Once the temperatures are appropriate, carefully pour the lye solution into the oils while stirring continuously. Use an immersion blender to blend the mixture until it reaches "trace," a pudding-like consistency.
If desired, add your essential oils at this stage and mix well to incorporate.
Pour the soap batter into molds, smoothing the top if necessary. Cover the molds with a towel to insulate and allow the soap to saponify for 24-48 hours.
After the soap has hardened, carefully remove it from the molds and cut it into bars. Place the bars on a rack and allow them to cure for 4-6 weeks before using.