Glazes are basically a type of glass which has been formulated to adhere to the surface of clay. They need to be designed to mature at the same temperature as the clay and have about the same coefficient of thermal expansion as the clay so they don't crack as the clay cools. On functional pots, glazes must be smooth, durable and easy to clean. Glazes usually have color or surface aesthetics which the potter finds to be a positive addition to the overall beauty of the pot she or he is making. Glazes also help to make a pot water proof; although this is more important in earthenware than it is in stoneware or porcelain. With all these requirements it is easy to understand why some potters are protective of their glaze recipes. Others feel that the beauty of their pot comes from far more than the glaze composition and they share their glaze recipes freely. Glaze formulation is not an exact science. While the basic chemistry is understood, obtaining the right balance of all the above characteristics requires a lot of experimentation. Using the computer (or doing it by hand) to calculate the relative ratios of the oxides in a glaze, though, can substantially cut down on the amount of experimentation that must be done. There are several computer programs available to potters to aid in this task--the one I wrote (GlazeMaster™) combines the capabilities of being an excellent glaze recipe database and providing the calculations of glaze composition a potter needs to shorten the glaze development process.
The three essential ingredients of a glaze are silica which is the glass forming component; flux which aids in melting of the glaze; and alumina which gives stability to the glaze. Getting the right balance of these essential ingredients involves mixing various minerals (e.g. feldspars, lime, talc, clay, sand and others) together and adding appropriate metal oxides for color. There are rules of thumb and even computer programs to help do this with less trial and error; however the only result that counts is seen by putting the glaze on a pot and firing it to see what it looks like. Potters can also buy preformulated glazes from ceramic suppliers; however I would wager that most give this up very early in their career as a potter. Formulating your own glazes is exciting, is one of the distinguishing characteristics of a potter's work, and gives you more control over your work. In addition to changing the glaze formulation itself, exciting and beautiful results can be obtained by using two or more glazes in layers or side-by-side.