Materials:
Hard-boiled eggs
vinegar
Cool Whip
food dye (use a gel like this one)
tray wrapped in aluminum foil
wood stick or toothpick
gloves
paper towels

Soak the hard-boiled eggs in vinegar for about 5 minutes.  This will help the dye set better on the eggs.  Once taken out, wipe each one dry.

Spread a 1 inch layer of Cool Whip onto a tray.  I used about 1.5 containers of Cool Whip.

Squeeze a few drops of food dye onto the Cool Whip.

Use a thin wood stick or toothpick to marble the dye throughout the Cool Whip.  Do not over-marble if you want to keep your lines and colors distinct.

Place the egg on the Cool Whip and roll it across until all sides of the egg are covered (wear gloves to protect your fingers from getting dyed).  As you do this, you’ll see that the lines of food dye flatten and smear onto the egg, becoming larger and therefore potentially a lot more muddy than you intended. 

Lay each egg on a plate, still covered in the Cool Whip, and let the dye set for about 20-25 minutes.  If you’re using colors other than black, you can rinse off the eggs after the setting time by lightly shaking each one in a large bowl of water without rubbing.  This will make the color fainter than how it looked with the Cool Whip, the benefit being that the surface is now more colorfast and cleaner to handle.  Follow the next steps if you’d rather maintain color vibrancy or are using black dye.

At the end of the setting period, wrap each egg in a paper towel and gently squeeze all over the surface to dry (do not rub).  You’re pressing the dye pattern into the egg while absorbing the Cool Whip and excess dye into the paper towel.  Keep doing this while continually moving the egg to clean portions of the paper towel until barely or no dye is coming off.  Repeat until as much excess substance as possible is removed