I hand dye nearly all of the fabric that I use in my art work, because of the depth that it adds. My methods can very but for the most part I use RIT dye and follow the stove top direction on the box.
I have found that you can achieve a great range of color when you combine different fabrics that very in fabric content as well as weight bellow are my results using 4 different dye baths.
Because I dye almost everything that I use the fabrics I gravitate to buy are white or natural in color for the most part. But you can even dye things that are different colors for a even more unexpected effect.