After watching Martha do this for years, I finally tried it out. These aren't the best photos, but they are the real deal pics from my house.
First, you have to find a bunch of silk ties to cut up (Salvation Army, Goodwill, ask friends).
Cut the ties up - you need squares of just the silk design part, discard the rest. You should be able to get enough silk from each tie to do 2-3 eggs at least.
Face the good side of the tie fabric IN and wrap around the egg. Secure with a rubber band or tie tight with string.
I don't have a good shot of this here, but if you want to do multiple eggs, also wrap with a piece of muslin or cotton (like an old sheet cut up). This is what you see in boiling pot photo.
Boil for about 15 minutes.
Again, I don't eat the eggs.
Once cooled, cross your fingers and unwrap!
Be ready for the design to transfer in its own way. It won't be an even transfer - but it is really cool.
Martha says 20 minutes and you can eat the eggs: http://www.marthastewart.com/269788/silk-tie-easter-eggs