You will need...
Safety Goggles and heavy duty gloves (washing up gloves will do)
Apron and old long sleeved shirt or top and sensible shoes (open toes are not a good idea in case of spills!)
The Soap Pot or container - which should be made of a sturdy plastic or glass (Pyrex - heat resistant glass) or stainless steel (NEVER USE ALUMINIUM, TIN, IRON OR ANY ITEMS WITH SPECIAL NON STICK COATINGS as they will react with the caustic soda). Ensure that the pot is large enough to contain all your ingredients plus room to stir without spilling.
The Lye Pot or container - which also should be made of either sturdy plastic or glass (Pyrex - heat resistant glass) or stainless steel (NEVER USE ALUMINIUM, TIN, IRON OR ANY ITEMS WITH SPECIAL NON STICK COATINGS).
Something for stirring - Stainless steel Balloon Whisk or Spoon or silicone spatula, spoon or paddle. Again, avoid aluminium or thin plastics or products with special non stick coatings. An electric stick blender is very useful to speed up the length of time it takes to stir the mixture.. but should not be considered essential soap making equipment.
A smaller glass or plastic container for the Dry Sodium hydroxide.
You actually do not need to spend a lot of money on special soap making equipment, you could go VERY basic. This is what we used when I taught soap making in Nigeria, most of the people learning how to make soap could not afford any expensive equipment, as you see... it was a couple of plastic buckets (sturdy plastic), and a long handled spoon with an optional silicone spatula.
Thermometer (Avoid those with plastic or aluminium mountings) This is desireable...but not essential... you could simply go by feeling the outside of the jug to assess if it is 'cool' enough... but realistically... if you are a beginner, you won't know what 'cool' enough feels like
You will also need Greaseproof or waxed paperfor lining your mould (mold). You can use practically any container as a mould. A shoebox can be lined with silicone paper or a plastic ice cream container can be very useful... even easier, cut off the top of a milk or juice carton (the ones that are lined with a plastic like substance inside) and use that - once the soap is set you simply tear or cut it off and discard.
TIP If you decide to use a plastic mold you won't necessarily need to bother about lining it. But be warned... cold process soap sticks! If you find you cant get the soap out of the mold the next day you simply pop it into the fridge for a while to get cold. It should pop right out then.
A couple of towels or old blankets will be needed for insulating the soap overnight if you live in a temperate climate. But not essential because sometimes, depending upon the recipe you don't need to insulate it at all!
That just about covers all the soapmaking equipment that you will need... it won't come close to covering all the soapmaking equipment that you will want!! Are you ready to begin?