I dyed several 100 yd skeins of a sport weight yarn that I bought on a cone years ago from Webs. The plan is to make very colorful mittens, from a book called Magnificent Mittens and Socks, by Anna Zilboorg. The gauge for her fancy mittens is about 6 stitches to the inch, which is perfect for this sport weight yarn.
I did all the dyeing in a crock pot out on the porch. This is a dedicated dye crock pot, and it works very well for dyeing wool, because it just sort of simmers rather than coming to a hard boil, which is easier on the wool. The workflow is: I skein the yarn, put it in soapy water to soak, heat up the crock pot, add the dye, add the yarn, and then wait a while for the yarn to soak up some of the dye. Then I add the vinegar which activates the dye and makes it stick to the yarn. I leave the mixture to simmer for a while, and then I come back and check it. If the water is clear, the dye has set and you can remove the yarn from the pot. I cool it for a minute and then rinse it in warm water, spin out the extra water and hang to dry.
I use the dye as a 1% solution. That is, I dissolve 1 gram of the dye in 100 mls of water, in a little half pint jam jar. For a deep shade, I use a 2% dye concentration: that is, I weigh the fiber dry, and multiply by 2 to get the number of ml to use to dye with. For example, for 50 grams of yarn you would use 100 ml of dye solution.
One thing I found out is that when you try to dye wool a deep shade like that, it doesn't take up every bit of the dye even if you cook it for a while. But that's ok, because if you put a new skein in after you take the previous, deeply dyed one out, the new skein will soak up the rest of the dye and will be a nice pale shade, a tint of the previous skein. These skeins harmonize well with each other in knitting.