Textile dyeing is awesome
We do it a lot for the re-enactment stuff, because it's cheaper to dye a white wool fabric then to search for an all ready dyed version of it.
You can use all sorts of natural stuff to dye your fabric with.
Besides that you have to keep in mind that a fabric made of wool (so woven out of any hair/skin) will have a more nice and well dyed color then when you dye a fabric like linen or coton (or any other plant) or any synthetic fabric. Fabric made out of plants or 'plastic' and such is far less likely to get the color you're aiming for. This is because of the difference in structure of the thread with which the fabric is woven.
Anyway, I know a few more things and websites with techniques and such but have to get back to schoolwork right now