Fiber content of most fabrics can be identified by conducting a very simple burn test. Take a small fragment of fabric, and hold in a pair of kitchen tongs over a kitchen sink and ignite one end and let the test piece burn back for a distance of about 2 centimeters or one inch.
Different fabrics will behave in different ways. For instance cotton will burn with a flame, smells like paper and produces a black powdery ash whereas polyester will burn (or splutter and burn) giving off a black flame and produces a hard ridge of ash which has a sheen to it. Wool burns with an orange flame and will smell like hair. Acetate will sizzle and leave a black bead behind.
How do you keep track of this information? Fiber identification charts are online at a number of sources. A Fiber Identification Burn Test chart is useful to have pasted at the front of a visual journal or kept on the studio wall pinboard by anyone who works with fabrics particularly if you want to clean or dye fabrics. Another chart is here and an article from fabric.net should provide most home dyers with the information they need.
If you need to know the meaning of fabric care symbols before you clean a garment Fabriclink have provided a chart. Their stain removal guides are also particularly useful as they have indexed the information according to the stain you need to remove.