Tye-dying is a fun activity for kids, and is popular at summer camps and scouting events. You can tie-dye all kinds of materials from shirts and shorts to socks and bandannas. However, once dyed, the colors can run if not handled properly, and handling depends on the type of dye used.
No matter what type of dye is used, after dying, leave the cloth alone for up to 1 day. This allows the dye a chance to bond with the material as much as possible. Don't undo the ties holding the material in its twisted state during this time. After the waiting period is over, untie the cloth and spread it out to dry completely. It is best to lay it on plastic for this so the dye doesn't transfer to something else.
If the dye that was used is listed as a fiber reactive dye, then it was made to bond with fabric. This means that the dye will not fade out when washed. It has bonded with the material properly. However, with the amount of dye used to tie-dye, there is no way that all the dye will attach to the material because the material will only hold so much. This means that there is loose dye on the fabric that needs to be washed out. Wash the shirt in cold water to keep bleeding of material to a minimum. Also use a synthrapol detergent. This will keep the loose dye in the water from settling on other less-saturated parts of the material. Not much is needed: it only takes 1/4 cup for a full load.
If the dye is not fiber reactive, the dye will not completely bond to the material. Even after it sits for a while, it will need something to set it into the fabric permanently. Vinegar is a good way to do this. Wash a full load with 1 cup of white vinegar. The vinegar will set the dye in place.
Take a few precautions when working with dyed materials. Wear gloves before washing the material to keep the dye from transferring to your skin. Before and even after washing, use plastic between any layers so that ink from one part of the cloth won't transfer to another. An example would be putting plastic inside a shirt so that ink from the front doesn't affect the design on the back. Also, sometimes you'll need to wash the material several times before it can be thrown in the regular wash with other clothing.