Determine if your fabric is a "cellulose" fiber, or a "protein" fiber.
Step2
Look at the tag. If the tag says: cotton, rayon, linen, bamboo, or hemp the fabric is a "cellulose" fiber. This means it was made from plant/tree fiber.
Step3
The best dye types to use on cellulose fabric are Fiber Reactive dyes. These dyes penetrate each thread of the fabric and dye it permanently and are fade resistant. There are several kinds of fiber reactive dyes. I recommend Procion MX fiber reactive dyes. They are cold-water dyes (literally) which makes them more flexible than most dyes.
Step4
If the tag on the fabric said silk, or wool it is a "protein fiber". This means it came from an animal.
Step5
Acid Dyes work wonders on protein fibers, but can be trickier to use than fiber reactive dyes. Acid dyes need to be watched carefully, or at least timed accurately. Acid dyes require hot to boiling water and frequent stirring.
Step6
If you want a dark color on silk, or if you want to dye wool any color, acid dyes are the way to go. However, I have had very good results with fiber reactive dyes on silk, but only in lighter colors, or when I was experimenting.
Tips & Warnings
Read my article "How to Mix Procion MX Fiber Reactive Dyes" for more tips
Fabrics that are blends of two types of fiber will not necessarily follow these rules.
When in doubt, contact the maker of the fabric, or the manufacturer of the dye and ask questions!
Always follow the manufacturer's directions while fabric dyeing.
Enthusiast 
Comments
grouch said
on 1/7/2008 Thanks for all the information. I never knew the type of fabric made that much of a difference. Thanks again.