In order to learn how to temper chocolate we need to first understand the chemistry and molecular structure of it. Chocolate, simply put is cocoa solids suspended in fat (cocoa butter) molecules/crystals, so really when you melt in order to temper chocolate, you melt and temper the cocoa butter, which causes the chocolate to look shiny, with a snap and a great flavor. Tempering is restructuring the fat molecules.
Cocoa butter contains six different types of crystals, and only one of them is responsible for the best temper in chocolate, which is called the beta crystal or form V, form VI is also strong crystals but only small amounts are formed. Out of temper chocolate has more of the bad crystals in it than the good ones, and chocolate does fall out of temper over time. This makes chocolate look dull, sometimes with white spots (bloomed), and tastes off and has a chalky texture. In order to temper this and create the beta crystals you need to melt the chocolate to destroy all the crystals, as a general rule melt dark chocolate at 115-120 F, white and milk between 111 – 113 F, then you have to cool the melted chocolate down to between 84-89 F.
There are two types of tempering, seeding method or the classic method of using a tempering stone, typically a slab of granite or marble.
In this method, melt only about 2/3 of the chocolate you plan to temper on a bain-Marie (double boiler) or using a microwave, to no more than 120 F. At this temperature the cocoa butter crystals loose their shape and become unstable. Now to cool the chocolate you use the remainder un-melted chocolate, stir in a bit at a time and monitor the temperature using a laser thermometer. Your chocolate will be in temper between 84-89 degrees, which means the cocoa butter crystals are mostly the beta type, with a small percentage of the less strong crystals, at this point you can use this chocolate, however if you want a perfect temper, you need to cool it all the way down to 84 F, then gently heat it back up to 88-89F, this will get rid of the rest of unwanted crystals. You have to make sure that your chocolate stays between 84-89F while you work with it. The easiest way to raise the temperature slightly is to use a heat gun or a hair dryer for a few seconds.
Tempering stone method:
Melt all your chocolate to the specified temperature, pour 2/3 of it on a granite or marble slab and keep the rest at the melted temperature. Repeatedly fold the chocolate onto itself and spread it across the granite until the chocolate is a uniform 82°F (28°C). The chocolate needs to be worked sufficiently on the granite slab for enough seed crystals to form, so you have to work relatively fast as the chocolate cools. A good way to tell when you've reached the right temperature is to pay attention to the viscosity of the chocolate. When the chocolate begins to thicken a little, seed crystals are forming and you should be able to reincorporate it into the rest of the chocolate. The tempered chocolate must then be kept at tempering temperature, 88-89°F (31-32°C) until used.