With my experience, you'd need to do it in a pot on the stove, because you have to "cook" it to make it absorb the color and set the dye.
If you use Kool-Aid, just use one packet for each ounce of yarn.
You would put the Kool-Aid in the water, stir to dissolve, then add the yarn and let it cook until the water turns clear, then remove the yarn.
Then add more Kool-Aid, stir to dissolve, then add yarn again, and cook til the water turns clear again, remove the yarn.....
Over and over, til all the skeins are dyed.
If you always use the same amounts of Kool-Aid and yarn, it should all turn out the same color.
Of course, this is for a single color of yarn. I don't know how to do the variegated stuff.
Here are some online tutorials: