You'll need plain white cotton cloth, either just pieces of cloth or white T-shirts (but make sure they are 100 percent cotton!), and dye - the most commonly used kind is RIT dye. And you'll need wax and paintbrushes and an iron. Melted crayon ends will be fine, or you can buy paraffin in sticks. Follow the instructions on the RIT dye to make up the dye. Melt the wax or crayons by putting it in a metal can and putting the can in a saucepan full of water, then heating the water on a stove.
Then dip the paintbrush in the melted wax and paint designs on your cloth. Make sure the wax is pretty thick so it will block the dye. Remember, the dye will color wherever you don't put wax, so you are painting in white on a dark background. When you are done painting your design, dip the cloth in the dye according to the directions on the dye. If you are going to dye your cloth more than one color, do the lightest color first (usually yellow).
Now let the cloth dry (on a line, not in a dryer! It will get dye all over your dryer). When it is dry, put the cloth on a section of newspaper, with some paper towels between the cloth and the newspaper, and iron the cloth until the wax melts and comes out.
If you want more colors, you will need to paint on more wax and redye the cloth now. When you are done, iron the wax out again. Make sure to fix the dye according to the directions, before you wash it, or the dye will run.