Cold Process: This is the basic method of making soap from scratch, by mixing lye, water, and oils. Some people recoil at the thought of lye, but actually all soap is made with lye. The FDA defines soap as having been made with lye, otherwise it is a detergent bar or some other type of cleanser.
There are two reasons for lye's (and soap's) spotty reputation. One is memories of great-grandmother's lye soap, which could often be made with too much (or too little) lye due to inconsistently produced lye and/or imprecise measurements. The other reason is cheap supermarket mass-produced soaps, which usually have the beneficial glycerin removed and sold off separately for greater profit, and to reduce soap shipping costs. These dry bars are unnourishing and can contain irritating detergents and/or cheap fragrances. Handmade soap today can be made with precise lye measurements to achieve just the right ph for the skin, and of course leaving the glycerin in for the benefit of your skin.
This method is called "cold process" because no cooking is involved; you don't add heat at all (except possibly to melt solid oils for mixing -- more on that later). The chemical reaction of lye plus oils creates its own heat. Soap can be made with almost any type or combination of vegetable oils or animal fats. First, lye (sodium hydroxide) is dissolved in a small amount of water. This causes the water to heat up right away, due to the exothermic reaction. After waiting some time for the solution to cool down, we then combine this mixture with the chosen oils or fats. If using oils that are solid at room temp (such as coconut oil, lard, etc), we would first melt the oil so everything is liquid for mixing. The mixture is then stirred vigorously; this is where an immersion blender (aka stick blender) is a huge time saver. In a way, oil and water are being emulsified, with lye as the emulsifier. After 5 or 10 minutes of stick blending, the soap begins to "trace". This means it begins to thicken, and will thickly coat a spoon. Then it is time to pour into a mold before it sets in the mixing bowl. Generally there is plenty of time to get the soap into the mold (kind of like mixing pudding and pouring into a pie shell). However some additives such as certain fragrance oils have the effect of speeding up trace, in which case you have to get the soap into the mold quickly.
Once in the mold you should generally insulate by putting a blanket around the mold, to help keep in the heat that is generated. The soap goes through "gel stage", a period where it becomes translucent from the heat. At this point the ph of the soap is coming down and the lye is being fully consumed in the process. If it was measured correctly, no lye will remain; it is all converted to soap and glycerin molecules. The next day, the soap should be still somewhat soft, but hard enough to remove from the mold and cut. Then curing time begins - generally about 3 weeks for the bar to harden, dry, and ensure the ph is milder still. Bars should be set standing up on a shelf or wire rack for curing.
Hot Process: Hot Process is similar to Cold Process, except that in this case the liquid oil/lye mixture is cooked in a pot on the stove. This speeds up the soapmaking chemical process. The main advantage of this is that the soap needs much less curing time and can generally be used the very next day. Another advantage is that fragrance or essentials oils can be added later in the process, after the chemical reaction has largely taken place (but the mixture is still liquid, enabling you to mix in the scent). This is much easier on the scents so you get less scent fading than with cold process. The disadvantage in our opinion is that the resulting texture of the soap is grainier and less smooth.
Cold Process Oven Process (CPOP): CPOP is similar to Cold Process, except that gel stage is "accelerated" by pouring the soap into a pan that can go ino an oven. It is then cooked at low oven temps in order to complete the gel stage faster, resulting in soap that many say can be cut and used the next day, instead of waiting for the normal curing time. We have not used this process ourselves but some soapmakers use it regularly.
Melt & Pour Soap: Melt & Pour Soap is sometimes called "Glycerin Soap" although that is a misnomer, because all soap contains glyercin (unless it is removed, as with corporate soaps). There is also a myth that this soap is not made with lye. The crafter selling the soap bars may not have ever used lye, but when the base was made, it was made with lye. Melt & Pour is more soapcrafting than soapmaking, since you are using pre-made blocks of soap, melting it down and adding scents, colorants, and/or other additives. MP Soap is sold in small or large blocks of transparent or opaque soap. The opaque varieties are usually white and colored with titanium dioxide. It can be repeatedly melted (in a microwave or double boiler) and remolded, with the addition of pigments or liquid dyes, fragrance or essential oils, and any other additions your imagination can come up with.