In a simple 1-step process using readily-available starting materials I show how you can make your very own soap. The soap can be cast into the shape of your choice: I have elected to make Virgin Mary Soap.
Step 1: Purchase Raw Materials
You're going to need a large quantity of coconut oil, palm oil, sodium hydroxide, and fragerence (usually an essential oil). These materials can be acquired from the "internet."
Step 2: Prepare the Sodium Hydroxide Solution
Weight out 85 grams of sodium hydroxide (achtung! gloves!) and dissolve it in 240 mL of distilled water. It will get extremely hot. Try not to spill it on your pants.
Step 3: Weigh Out the Fat
Into a big beaker (1 L or larger) weight out 170 grams of coconut oil and 440 grams of palm oil. If for some reason you don't have professional laboratory glassware you could use stainless steel cookware (NOT aluminum).
Step 4: Get the Fats & NaOH to the Right Temperature
The idea here is to get both the fats and the NaOH solution to around 50 ºC at the same time. While you are waiting for the NaOH solution to cool you can start heating the fats, which will melt and become clear.
Step 5: Add the NaOH to the Fats
When both solutions are ~50 ºC, add the NaOH solution to the fats. Stir it up really well for about 10 minutes, then periodically thereafter. The mixture will get cloudy and lighter in color as they react.
Step 6: Wait Until the Soap Traces
You can tell that the soap has formed properly when it "traces." This describes a state where, if you drop a bit onto the surface it will leave an indentation for a moment, and if you drag a spatula across it will leave a trail. This takes around 45 minutes.
Step 7: Prepare the Mold
While you are waiting for the soap to trace, get your mold ready. Here I am using what is actually a candle mold for the Virgin Mary. This too can be purchased off the "internet." Get the mold sealed properly and clamped upside down.
Step 8: Add Fragerence
Once the soap has traced, stir in the fragerence of your choice. I am using 12 mL of a "lavender and apples" scented soap fragerence. You could also use an essential oil here.
Step 9: Pour the Soap Into the Mold, Wait, Then Unmold
Pour the liquid soap into the mold, then put it in a safe place and don't touch it for 48 hours. Then you can unmold your soap and admire your creation. Cut away excess flashing.
Step 10: Enjoy Your Soap! (but Not for 3 Weeks)
Congratulations, you have now made some bomb-ass soap. However don't try to use it right away. The sodium hydroxide takes a while to be fully consumed as it reacts with the fat. Wait a few weeks before using it. You can monitor the progress of your soap by checking the pH which will drop from 14 (first image) to 10 (second image). Good soap is pH 7-9.