Decorating eggs with bright colors and patterns is simply fun to do, even if you don't celebrate Easter—the same way people from any faith tradition can enjoy squishy marshmallow chicks and biting the ears off chocolate rabbits.
Likewise, you don't have to be Ukrainian to make Ukrainian Easter eggs, or pysanky, which means "to write." Created in a manner similar to batik fabrics, the eggs are layered with different colored dyes and wax to form designs.
Like many folk Christian traditions, Ukrainian egg decorating can be traced to Pagan times, when eggs symbolized eternity and pysanky in particular maintained the balance between good and evil in the world.
My relatives used to make them; the eggs, which have their yolks blown out through a pinhole, keep forever and have even been passed down in the family. If you're bored of solid-colored eggs and can supervise the use of hot wax around young children, you can embed your own symbols into eggs.
Many of the ingredients might be found in your kitchen or around the house: eggs, beeswax (don't use regular wax candles), plant sources for dyes. If you use all-natural dyes, it's probably safe to hard-boil the eggs as usual and then apply the layers of beeswax and color. If you're nervous about eating an egg with some wax on its shell, blow out the egg's contents according to the instructions, using it for cooking.
Start with natural dyes. You can create custom colors without the artificial ingredients found in store-bought packets, which also don't have the dark you'll need for maximum effect.
Use vinegar while boiling for darker colors. Herbs, spices, and canned goods are all good sources of color. See this chart for creating more vegetable colors.
Decorating the eggs can be as simple or complex as you want to make it. Take a look at this overview of traditional Ukrainian symbols for inspiration, or create your own based upon shapes and images meaningful to you.
For intricate designs, you will need a special tool called a kistka—this stylus for drawing with hot beeswax is available in most craft stores. For more free-flowing designs and swirls, you can probably do without a kistka, substituting an orange stick or pin that will push the wax across the egg's surface.