Once you're ready to start marbleizing, stir 1 tsp to 1 Tbsp of oil into a cup of egg dye. Quickly dip your egg in and out of the dye. The dye will adhere, the oil will repel, creating the marble design. Keep dipping for more intense colors.
You can also let the egg dry and re-dip in a second color. Repeat as many times as you feel will make a gorgeous egg. When finished and the egg is dry, take a paper towel to get the excess oil off of the surface of the egg.
Different amounts of oil will result in more or less marbling. Experiment to find the mixture you like best. Remember you can always add more, so start conservatively.
Source: Enigma Communications, fabulousfoods.com