SLIDES USED IN THIS EXERCISE: 1208, 123, 148, 1-23, 8A, 3-88, 30, 3-61, 100A, 538, 552, 2-37, 674, 1193, 1-40, 54
There are, literally, thousands of staining routines. Some of the more common ones are listed below. Some stains are "general" in that they show you cellular architecture, others are more specific, delineating certain chemical components (e.g., lipid or carbohydrate) or even specific molecules (this is done by immunologically recognizing the molecule in question with an appropriate antibody and "tagging" it with something that's microscopically visible). The three stains you'll see and use most often are H&E (a general structural stain); PAS (a routine for recognizing carbohydrates), and one of the stains for connective tissues, typically a Mallory's or Masson's stain.
Why are sections stained at all? The answer to this question is that cytoplasm has about the same refractive index as glass. That means that details of cellular structure are more or less invisible unless something is done to make them visible. The stains are essentially a means of adding contrast to them.
One of the great advances of 19th Century biological technique was the discovery that cells and their parts could be visualized by staining; between about 1850 and 1950, innumerable papers were published reporting the specifics of what stain was useful for what cells and structures. This activity was greatest in Germany, where the growth of the synthetic dye industry fortuitously coincided with the perfection of the optical microscope that could take advantage of the new dyes. Every time a new colored compound was reported in the chemical literature, someone applied it to tissue to see what would happen, and in many cases the results helped advance the study of cell structure*.
Stains act as color filters and work on a subtractive principle. For example, if a tissue component absorbs red-colored dyes, then any wavelengths of light other than reds are filtered out. The reds pass through and are visible to the observer. Blue dyes filter out anything but blue wavelengths, etc. Since the binding of the dye molecules is predictable based on their chemistry and that of the structures to which they're preferentially bound, it's possible to make confident statements about what it is you're seeing. This confidence is, of course, based on tens of thousands of experiments and millions of hours of investigation extending over more than a century, carried out by scientists all over the world. What is today routine technical methodology was at one time cutting-edge science.
*At one time, I tried developing a stain myself. I invented a dyeing process that turned everything grey. I named it "Caceci's Monochrome," but alas, the method wasn't published.