There are probably as many ways to dye fiber or felt as there are ways to felt. Each person develops their own techniques and what works for them. Many people use food dyes or Kool-aid crystals to dye wool. Animal fibers need what is called an acid dye when commercial dyes are used. The acid is used to help the fiber accept the dye better and is a fairly harmless substance such as vinegar, citric acid or acetic acid. Natural dyeing is another method that works to dye wool and other animal fibers.
Plant based fibers need a different type of commercial dye as acid dyes do not work well with these types of fiber. Fiber reactive dyes such as Procion are the best bet for dyeing plant-based fiber. Silk is an unusual fiber as it can be dyed either with acid dyes or fiber reactive dyes. Dyeing your own colors saves money and allows you to create your own palette of colors to use in felting.
Take a look at Karen’s tutorial for using food dyes.