While growing up the only method I knew for dying Easter eggs was to use PAAS dyes. Something about those slim boxes filled with little plastic cups and colored tablets excited me much more than they should have.
Now that I'm past the age where PAAS dyes are still exciting, here are some kitless egg-dying alternatives. The District Domestic has tips for dyeing eggs naturally by using red onions, cabbage, frozen blueberries, and turmeric. (What's Cooking America has more suggestions for natural dyes.) Barefoot Kitchen shows you how to make edible colored eggs with cracked patterns inspired by Chinese tea eggs. For other interesting patterns, Instructables has directions for dyeing eggs with onion peels. And if for some reason you have old, neglected silk ties lying around, Dollar Store Crafts shows you how you can use them to dye eggs.