I will start out with a few tips that I know from my grandmother that are good to know when doing this. First, it is best to color the eggs while they are still warm. The water in which the egg is dipped to be colored should also be quite warm and a tablespoon of vinegar is added to each container holding a color. Both of these help to achieve brighter and more saturated colors ( but needless to say the quality of the food coloring is important). When doing this, it usually requires that you boil between 15-20 eggs. That is to ensure that there is an egg for everyone who stops by as well as to compensate for some that might crack while boiling. Follow the usual procedure for boilng them ( bring them to room temperature, cover with cold water, put on the stove...), but my grandmother also puts a kitchen towel on the bottom of the pot and folds it in between the eggs in the water. When you go to remove the eggs from the water, do so one by one in between the folds.
You will also need to hunt down a lady's stocking or a pantyhose for this, the thinner the better. Cut a straight tube from it between 5-7 inches, depending on how stretchy it is, and tie a knot on one end. Prepare a few more like this and set them aside.
Assuming your eggs are boiled at this point, dissolve the colors in very warm water to be ready for dipping. I used several sour cream containers. Add the vinegar to the water along with the colors. Holding an egg in a dish towel, draw whatever design you like on it with a thin pencil. Redraw over the pencil line with the crayon. It is good if the crayon melts some while doing this. That will ensure it will fill the egg pores and won't allow the coloring to work there. If too much seems to remain on the egg surface, you can carefully scrape it off with the blade of a small knife. I prefer a neutral crayon, but you can use a color one if you like.
Place the egg in the prepared tied stocking, and tie a knot at the other end. Make the egg as tight inside as you can without breaking it, to ensure that it won't move around. This is easier to do if someone holds the knot at the bottom for you.
The next important thing is to think about the order in which you choose what colors to dip in. The variation is achieved by the overlapping of several colors. I first dipped the egg in the yellow about 3/4 of the way and let it sit for about 5 min. Then took it out and placed it in a slot in the empty egg carton to sit for another 5 min. Then carefully untied the top knot ( or just cut it off ), and take the egg out and let the yellow dry out. Place the dried egg in a clean sock and tie again as above. Dip the egg about 1/2 of the way into the blue color, but with the other side of the egg going in first. Hold it in another 5 min, let sit outside another 5 min, take it out of the sock and leave it in a clean slot on the carton to dry. For the last color (red) I just held the egg in the liquid with my hand as it only needed to be dipped abou 1/3 of the way.Then let it dry in the egg carton, placing it with the wet part downward, or your color will run down the side. At the top where the yellow didn't go, the egg was a turquoise blue. Below it where the blue and the yellow overlapped, it turned light green. Below it a band of yellow remained. And at the bottow the red and yellow combined to make an orange circle. This particular egg happened to have a sort of a defect on its shell ( calcium concentration I think) and I used it as a center to my flower design. After it was all done and dried, we found some children's stickers and I used the outside of a butterfly sticker and placed it there. I used a brown egg for this. If you have white ones, I assume there will be even more contrast between the colors.