The basic equipment you will need is:
Stainless steel stockpot for melting of oils and mixing of soap.
Heat resistant glass bowl or heavy duty plastic pitcher for mixing of lye water.
2 stiff rubber or silicone spatulas for mixing.
Hand blender and wire wisk for mixing.
Digital scale for accurate measuring of ingredients.
Kitchen thermometer to check temperature of oils and lye water.
Wood or plastic mold.
Butcher paper if using wood mold.
Safety goggles and gloves.

A basic one pound all vegetable soap recipe:
4 ounces Coconut Oil
4 ounces Palm Oil
8 ounces Olive Oil
2.2 ounces Sodium Hydroxide (Lye)
6 ounces Distilled Water
0.5 ounces Essential Oil

Step 1.
Place distilled water in plastic pail or glass bowl. Slowly add sodium hydroxide and stir gently. Allow to cool between 100 and 110 degrees farenheit.

Step 2. Place coconut and palm oils in stockpot and melt. Once melted add olive oil. Allow to cool between 100 and 110 degrees farenheit.

Step 3. While lye water and oils are cooling prepare your mold. If using a wood mold line with heavy duty wax paper (freezer paper) or trash bag.

Step 4. Once lye water and oils have cooled slowly pour lye water into pot with oil. Pour away from your body and take care not to splash as the lye water is still caustic.

Step 5. With wire wisk slowly begin stirring the lye water and oils. Continue for a count of 100. Begin mixing with hand blender and again count to 100. Alternate between the wire wisk and the hand bleder until the soap mixture reaches trace. Trace is when a drizzle from the spatula leaves a small trace of pattern before sinking back into the mixture.

Step 6. Add essential oil to soap base and stir well.

Step 7. Pour into prepared mold and cover. Wrap in a heavy towel or blanket to insulate the soap and leave undisturbed for 24 hours.

Step 8. After 24 hours you can unmold and cut your soap to allow it to cure. It is safe to touch at this point though it should not yet be used. With a standard kitchen knife cut into bars and place in a dry, well ventilated room for 3 to 6 weeks. This curing period is needed to make your soaps dryer, harder and milder to use.

Congratulations, you now have your own handmade soap!