The chemical reactions of acids and alkalis with the wood's own constituents give a deep-laid color which is comparatively inexpensive and (in most cases) lasts well. These are traditional stains, the only ones available before modern industrial chemistry, and are still used in antique restoration or where, say, new church furniture has to be matched to very old. White vinegar (acetic acid), if left with a handful of iron nails in it overnight, will turn oak almost black a matter of seconds after you apply it.
A stain made from potassium permanganate crystals dissolved in water will bring out a warm brown shade, and makes a good dye for floors because it is inexpensive, although it does fade. Potassium bichromate crystals, which are yellow and orange, dissolved in warm water, darken oak, ash, mahogany and other high tannic acid-content woods without affecting the basic color. Burnt sienna – a pigment – dissolves in stale beer and makes a very effective mahogany-colored stain; and there are many more.
If you want to mix your own stain, start with a decision about the colouring agent and the base, and then experiment. Pigments are really best for touching up over an already sealed surface; water as a medium will give you problems with raised grain; slow-drying oils are easiest to apply evenly, but may strike through a finish; spirit-based dyes dry very quickly. Keep a careful record of the proportions you are using, and always test.
Touching in, painting grain lines over stopping (wood filler) and so on, is best done with oil (white spirit) and pigments – artist's oil pigments are fine. For french polishing, you can tint the finish by adding pigment or spirit aniline dyes to the shellac itself. Use a fine artist's brush, so that you can control exactly what color goes where. Cellulose and synthetic lacquers have their own tinters. These fine touches should always be sealed on top; the order is stain, sealer, touch-in, finishing coats.
Colored varnishes are already pigmented, and can be used to carry more. Used on their own, they are popular because they are not difficult to mix or apply but they are a quick compromise solution, and show up as such. There is nothing to recommend them in terms of appearance, in that they combine uneven pigment spread with the thick 'plastic on top' look of poly-urethane. These too should be given a top coat of clear varnish or polyurethane, which you are using.