There are a few tutorials for this online and all are pretty much the same. The important thing here though is to NOT roll the eggs more than a couple times. Any more and you end up with solid color eggs.

What you’ll need:
hard boiled eggs
white vinegar
food coloring
colander
paper towels
rubber gloves

Put a few eggs into the colander and splash with white vinegar. Starting with your lightest color, put one drop of food coloring onto each egg. Roll around the colander just a couple times. Take your second color and place a drop on each egg and roll a few more times. Let sit for 5 minutes for the dye to set. Rinse under cold running water. Pat dry with a paper towel and let fully dry for at least an hour.

A few notes:
-wear rubber gloves if you don’t want dye on your hands. It stays on the skin for a few days.
-put plastic wrap on your counter under where you’ll be drying the eggs. The dye tends to stain the counter tops.
-don’t use more than 2 colors per egg. I tried 3 and the colors became too blended.
-only place a few eggs in the colander at a time. Too many and they break the shells.
-make sure you let them sit the full 5 minutes. Any less time and the colors will be pastel and muted (which is fine if you’re going after that look).
-and have fun!