DLTK's Crafts for Kids
Food Coloring Dyed Easter Eggs

I find this method easier and cheaper than the store bought tablets.  I also find it cleaner than some of the varieties that they sell now (we tried the sponge ones one year...  It was fun, but incredibly messy)

Suggestion from April:
"Here is an idea for Easter Eggs for toddlers. Use spray bottles with color water & let the toddler spray the eggs. Eggs can either be white or already dyed.  This way, they can participate as well.  The eggs turn out beautifully." 
Thanks April
 

Materials:

• hard boiled egg(s)
• vinegar (plain white)
• small bowls, cups or empty margarine containers
• water
• food color drops

Instructions:

• fill containers about 1/2 to 2/3 full of water.  Don't full TOO full or when you put the eggs in it will overflow.  I like using cups because it's the most frugal *grin*.
• Add 1 tsp of vinegar (for every 1 cup - ish of water.  We don't need absolute measurements here, but if you're using a gallon ice cream pail you'll need more vinegar than if you're using a teacup).
• Add drops of food color until you're happy with the hue.  (I usually get happy with the hue and then add 2 more drops...  I find that tends to make the eggs the color I was originally happy with).
• Put hard boiled eggs in the cups (I use a Tbsp to put them in and take them out).
• Let dry.  Wipe with vegetable oil (with paper towel or a rag) to make a glossier egg.

NOTE:  I always cover my work surface with newspaper so the dye doesn't get on my kitchen table.  If it does get on furniture, wipe it off with a rag immediately.  This goes for the store bought packages too.

Printable version of these instructions