I saw this on a blog and wanted to test drive it :) I got 3 100% silk ties from DI (I've found that the deeper and more detailed the design the better the dye), a few eggs and some dental floss. And Javin and his OJ.
I cut the ties apart, laid them flat and wrapped them around the egg. You should be able to dye 4-5 eggs per tie. Keep the white insides of the tie, you'll use them later.
If you've ever tried to wrap a round gift its tough - this won't be a walk in the park. I found it easiest to twist ends of the fabric and tie them closed with dental floss (you can use string/thread, but floss is a little easier to control because its a sticky). Then wrap the floss around and around the egg to get the fabric as close to the egg as possible.
Then wrap the fabric covered egg with the white tie liner the same way you wrapped it before.
Boil for 20 minutes, cool for 10 minutes in cold water. Gently cut away the fabric when cool. I think the paisley one turned out best :)