There are several places that say vinegar makes the yarn take dye better, and that heat does the same. So for safety's sake, I used tons of vinegar and heat. Not sure if this is really necessary, but it's what I did and you can to! =P My materials for this process are below, plus things you have around your house like forks, paper towels, cling wrap, and paper plates. I used a stainless steel pot for all the process instead of using a ton of bowls. Also included in the picture are white vinegar, Kool Aid packets, and Peaches & Creme yarn.
First, I took about half the skein of yarn and wrapped it around a couple dining room chairs. I left the other half in a ball and used that for another yarn dyeing experiment that I will chronicle later. I made a mixture of half vinegar, half warm water and threw the yarn in. It floats, so I had to smash it down in there with a fork. I let it soak for a while on one side, then flipped it over and let the other side soak.
I took the vinegar-soaked yarn out of the pot and let it drip over the sink for a minute. Then I laid it out on some paper towels to let some of the vinegar leave the yarn. I then unwound the ball and repeated the dining room chair process to make it easier to dry completely. I hung each one on a hanger to dry. You can tell from the pictures that the ball-soaked yarn (on the left) is actually smoother than the wrinkly, loose-soaked yarn (on the right). I let these dry overnight since I started out pretty late.
The next morning, I heated up some more water in a pot to almost boiling. I added a little bit of vinegar (didn't measure, just poured) and 2 packets of green Kool Aid (Lemon Lime flavor). Then I threw the yarn in, smushed it down a little with the fork, and let it soak. I flipped it a few times to help both sides soak up as much dye as possible. You can tell from the second picture to the third that it really began to soak up the Kool Aid. I've read in some places that the yarn will soak it all up and the water will be clear, but since I used 2 packets it never got clear. I may have over-estimated the Kool Aid to yarn ratio, but I wanted to be sure that I had enough dye.
I used the fork to remove the yarn from the pot because the water was still a little warm. I let it hang over the sink for a bit to drip and then moved it onto some plastic wrap. Like I said, I've heard heat helps this process and I'm not sure it's necessary, but I wrapped the yarn up in the cling wrap and put it in the microwave for a minute (just in case... couldn't hurt, right?). Then I removed the plastic wrap from my steaming yarn burrito, moved it apart and left it on a paper plate to cool and dry. When it was dry enough to not drip, I hung it on a hanger again to dry.
My second little experiment used the leftover (ball-soaked) yarn and some more Kool Aid. I added another packet to the leftover green Kool Aid mixture from the green yarn dyeing. Then I hung each end of the ball-soaked yarn into the pot and let the middle hang over. I smashed it down with the fork and flipped it over several times as in the previous example. Then I took it out of the pot and put it in the sink to drip. Then, for good measure, I poured the Kool Aid mixture over it so it would add some more dye to the yarn on its way down the drain.
Then I made another Kool Aid concoction. I heated water to almost boiling, poured in some vinegar, and mixed in 2 packets of red Kool Aid (Cherry flavor). Then the middle of the yarn section went into the pot with the ends hanging over. I let it soak with some white space in between the green-dyed portion and the water. Then I picked the yarn up by the ends and submerged it up to (and maybe a little over) the green dyed portion. That way, I was hoping it would end up variegated with really green and really red extremes with a pale green and pink in the middle.
I removed the yarn, dangled it over the sink, and poured the remaining Kool Aid over the yarn and down the drain. The yarn rested on a paper towel for a short period to sop up the remaining dye then went into a cling wrap burrito that was more like a churro because I didn't want the different colors touching. I put that burrito in the microwave for a minute to make sure it was hot enough, even though I've seen sources say heat doesn't matter. Then I arranged it loosely on a paper plate to dry.
I must warn you that by dyeing the yarn in a big heap I ended up with a tangled mess that took a while to get straight again. Here's a picture of the finished yarn. The red ended up more pastel after drying. I wrapped it around a toilet paper roll to keep it from tangling again.
Update: It has been a while since dyeing the yarn, and the colors fade a little bit over time. Also, washing the items I made removed much of the color. The unwashed items are still the same color I dyed them though! The red took to the cotton a lot better than the green did.