Dying your hair with Kool-Aid is actually fairly easy. All you will need are the following items:
- A small bowl
- 4-5 packages of Kool-Aid in the color that you want
- A bottle of hair conditioner
- Plastic wrap or some plastic bags
- Disposable gloves to protect your hands
Start by putting a small amount of conditioner in the bottom of the bowl. Microwave it for a few seconds to warm it up. Empty all of the Kool-Aid packets into the bowl and stir the mixture until the Kool-Aid is fully dissolved. Add a bit more conditioner until you have enough paste to cover your hair generously.
Although you can apply Kool-Aid to dark hair, you won't get very dramatic results. At best, you might get a hint of the color you are going for. For more noticeable results, you should use the Kool-Aid on light hair instead. If you already have blonde hair, you can just dye it as-is. If your hair is dark, however, you should consider pre-lightening it with blonde hair dye or bleach. This will allow you to get far more dramatic results.
To dye your hair, put on the gloves and begin to apply the paste that you mixed to your hair. If you are doing your whole head, apply it everywhere. If you are going for more of a highlighted effect, just apply it to the pieces of hair that you want colored. Be sure to wear the gloves the whole time or you will stain your fingers.
Once the mixture is applied to your hair, wrap it in plastic wrap or plastic bags. Not only will this help ensure that the dye doesn't get on anything, but it will also help keep the hair moist throughout the dying process.
In order for the dye to take effect, it is best to leave it processing overnight.  That means that you should wrap your hair in plastic well enough that the dye won't get on your pillow while you sleep.
When you get up in the morning, simply rinse the Kool-Aid out of your hair with clean water. Avoid using shampoo as much as possible since it will cause the color to fade more quickly. If you do need to wash your hair, try using a shampoo that is specifically designed for color treated hair in order to minimize the amount of fading. 
This video gives detailed instructions on the entire process: