Food colouring is a great way for kids to tie dye. Although it does not necessarily hold as well as other sorts of dyes, it is kid-safe and requires little supervision. Soaking the shirts in salt water after tie dying and washing them in cool water will make the dye set a little better, and some people really like the look of a faded tie-dye anyway.
Consider using actual clothing dye. Food colouring works well for food, but it can bleed and fade quickly in clothing, and it can only be used with certain fabrics.
Get a wool or silk shirt. Both of these textiles work fairly well with food colouring. Nylon also usually works well, but it sometimes has a synthetic coating on it that stops it from absorbing the ink. Cotton will not hold food colouring as well.
Soak the shirt in a mixture of half white vinegar and half water. You can also use water mixed with urea or most other acids. Wring the shirt out.
Tie knots in the shirt, or twist up parts of it and hold them with rubber bands. This will create bands and spiral patterns in the shirt.
Mix food colouring and water in bowls or condiment bottles. If you use bowls, dip the shirt in it. If you use condiment bottles, squirt them on the shirt.
Wrap the shirt in plastic and place it somewhere warm for about 8 hours. You could put it near a heat vent, or under a heating blanket. Be careful to not overheat it, particularly if you are using wool, nylon or something else prone to shrinkage.
Fill a bath with cool water and add salt, stirring until you can't get any more to dissolve. Wash the shirt in the cool salt water to set the dye.
Wash and dry the shirt as you normally would. It is now ready to wear.