These colorful eggs are made by applying alcohol inks to white plastic eggs. Since the inks are transparent, I like to use white eggs to get the pure pop of color. If you use pastel plastic eggs, the colors will be muted since the egg color will show through the ink colors. The plastic, non-porous surface allows the inks to spread and blend - if you apply to real eggshells, the inks will pretty quickly soak into the shell. Still beautiful, but you can't get the same type of texture. (And don't use alcohol inks on eggs you plan to eat - the alcohol soaks into the shell and can taint the egg inside).
The only retail store where I've found the white plastic eggs is Hobby Lobby, and only around Easter time. It's a package of 12 eggs that are two halves you put together. If not available at Hobby Lobby, you might find some on Amazon, but check that they are white glossy plastic, that they aren't hinged (with a strip of plastic holding the top piece and bottom piece together) and that they are really egg size (they sell a lot of minis).
To create these beautiful eggs, all you need is a selection of ink colors, and applicator tool and felt. Please check out my Alcohol Ink Supply List for a comprehensive list of products and links where to purchase. And here we go!