I've had some questions about how I dyed my Branching Out scarf, so here goes. Keep in mind that these comments apply to dying wools, not cottons.
I used ProChem dyes from a rug-hooking dye kit here: http://www.rugartsupply-suzi.com/proddetail.php?prod=s0012_PrimaryFusionDyeKit. [The picture above is from their web site.] You can also find some kits for dying on eBay, although they don't have the swatchettes or formula book. Dharma Trading Company (http://www.dharmatrading.com/) also has dyes and kits and a lot of other wonderful things.
The swatchettes are actually a bunch of dyed pieces of wool that show each formula in the book in eight grades or intensities of color. The kit comes with the basic CMYK colors (blue, red, yellow, and black more or less--it's actually cyan, magenta, and yellow) that you can use to dye millions of variations of colors. Yes, I also do rug hooking. :-) And there are 50+ swatches (not the four shown in the picture above). Here's a picture of my swatch set:
So here's what I did: I picked a swatch that had the color I was going for, used the book to figure out how much of each color dye to add, mixed it up in a plastic cup, soaked my scarf in some water with a bit of wetting agent (JetDry--the stuff you can get in the dishwashing detergent section of your local grocery-- or Synthropol, a chemical specifically for wetting fibers), then brought some water to just under boiling.
Then I put my swatch and scarf into the water and added the dye. The thing about dyes is that they don't absorb at the same rate; black will usually absorb first, so if you pull your item out of the dye bath too soon you get a gray color. Once you submerge it you can look through the water and see the color you want it to be, but that dye is still suspended in the water. So after an hour all the dyes are usually absorbed and you get the color you wanted. The more you stir and fiddle while the items are dying, the more uniform the color will be. Adding vinegar sets the color and you don't have to do much rinsing at all.
You can overdye colors you don't like, too! I figured that if I make stuff using light colors and hate the result, I can overdye them to the colors they want to be. I also would rather have splotchy areas of color instead of horizontal lines of color the way a lot of hand-dyed yarns knit up. My tastes will probably change, but that's what I like right now. :-)
The other nice thing about these dyes is that you can (most of the time) pull color out if you've totally messed up. It depends on the dye used, and sometimes it ends up grayed and even uglier, but there are ways to do it.
Color theory is one of those things that you really need to learn if you're going to get into dying. For example, say you've ended up with an acid green that you hate. What are you going to do? You can add a touch of red (green's complement) and make it more brown/gray, you can add more blue to make it more green (yellow and blue make green), or you can add more yellow and make it an acidy yellow. There are LOTS more options, but I'm not going to go into it in this post.
The ProChem dyes also work on nylon from what I've heard, although I can't verify that personally.
There's a LOT more to dying (and color theory), but a lot of it already exists out there on the net. If you really want to know more let me know.
A note about mixing dye powders: I mixed up all of my dye powder into a squeeze bottle (one for each of the four colors) using a specific ratio of dye powder to water, then I measure out the liquid for the formulas. It's not using them exactly as written in the book since most books use powder, but then I don't have to worry about 1/256th of a teaspoon measurement, either. The dyes have a MUCH longer mixed shelf-life--like a year, from what I've heard--than cotton dyes which are only good for about a day once they're mixed. The powders for dying need to be handled with care, like using a mask and not using food containers for dye powders or liquids.