The basics of wool dyeing...
Soak wool in lukewarm water with a good amount of white vinegar for about 20-30 minutes. Regardless of how you proceed, this is crucial. It thoroughly soaks the fibers so they will absorb the dye evenly and not splotchy.
Prep dye bath. What vessel you use is going to depend on how much you're dyeing. I use half gallon canning jars when I'm dyeing yarn, which hold a skein nicely, but probably wouldn't work for fabric - you need enough room for the fabric to be loose and "float" in the water. Most people will cut into shorter lengths or even diaper cuts before dyeing fabric for this reason.
Heat up some water - you want it warm, but not hot (be sure to leave room for the water level to rise when you add your fabric). Add a glug of vinegar to the water, and add your dye. I use basic food coloring, nothing fancy - and it wears just fine. Once you've stirred your dye in, then add your sopping wet fabric (don't wring it, just lift it out of the water and transfer it - the excess water helps prevent blotching), making sure the whole thing is submerged. Let the wool sit in the warm bath (over low heat) for at least 20 minutes. The longer you let the fabric sit in the dye bath, the less will rinse out, IME (i.e. if you just dunk it for a minute, most of it will rinse out, but if you let it sit for 20, little will rinse out). If the water turns clear and your fabric is not the color you wanted, lift the fabric back out, add more dye, stir it, then add the fabric back in. Let it sit another 20 minutes. You can do this as many times as you need to get the color you want, so long as you maintain the water temperature. You can also do it with different colors to get mottled coloring. I like to dye yellow and then overdye with pink - it comes out a pink/orange/yellow mottle that I find pleasing.
Yellow - requires a LOT of dye. Your bath should be like concentrated sunshine. I buy yellow dye separately rather than just using the little bottle in the mixed box.
Pretty much everything else doesn't require a whole lot of dye. Yellow is the weakest of them.
Don't bother with the black dye if you're trying to get black. It comes out a dark purpley-brown. It's a cool color, but it's definitely not black.
So, once you've gotten the fabric to the color you like, lift it out of the water bath, and transfer it to a bowl. Run your tap water until it is at least as hot as the water bath, if not a little hotter. Never go colder or you'll felt it. Rinse, rinse, rinse. If you're dyeing reds, it'll probably need more rinseing than any other color. Rinse until the water is clear. Don't let the water run onto the fabric, since that can also felt. Run it into the bowl, and gently swish it, dunk and lift.
Hang it to dry. I dry inside, so I put a bowl and a towel down to catch drips, since it will drip. If you're drying outside, do it in the shade.
If you don't want a solid color, you can dye in a tighter vessel and get a bit of a tie dye effect. If I cram 2 skeins into a single jar, I maintain patches of white, since the dye bath can't flow around the yarn. Then I can lift it out, bunch it in a different way and dunk it into another color, and keep doing that until I get the color I want. You can do true tie dyeing, but it is messy and not something I bother with.
