I always hollow out my eggs so I can treasure them for many years.
There is a very good tutorial here in eHow website that you can refer to.
I prefer to insert in the needle just about 5mm in the shell and not more to
prevent the shell from cracking. I make a few more holes very close to the
first one to create a larger hole and I repeat the process for the other end of the egg.
Blow the egg out as this tutorial says.
Or if you have a rubber ear syringe just do as Martha Stewart.
Make some colorful water with food coloring and a bit of vinegar.
I have used this recipe from Martha Stewart.
for a perfect submerge and to prevent your eggs from floating on the surface you need to
fill them with water. I used a medical syringe myself.
The best way to dry the eggs is to make a drying rack like this.
Voilà! Now you have perfectly dyed eggs!