Here's how I do it:
Get a 12 x 12 x 8" Priority box. Put a layer of styrofoam macaroni on the bottom.
Take a roll of bubble wrap. Pull off 8 pieces (it comes pre-scored.) Cut each piece in half so it's a strip about 4" wide and 8" long.
Take 8 pieces of paper towel, cut in quarters.
Wrap each egg in paper towel (I don't like the idea of the egg sitting right next to the plastic, want them to have a bit of room to breathe.)
Then roll the egg up in the layer of bubble wrap. Tape securely. Set in box with macaroni. Repeat.
Fill the remaining area with macaroni, making the whole thing very sturdy so nothing can move.
I can fit 15 eggs in one of those boxes. I always insure them. I used to write stuff on the outside, but have had better luck not doing that. According to a guy I know who works for the USPS, you don't want your package to stand out, you want it to blend right in. Sometimes stuff that stands out gets worse treatment, not better!
I should check with everyone I shipped eggs to this year to see what sort of hatch rate they got, have only heard back from two people. One woman got a 50% rate (and was unhappy about that, which seemed crazy to me.) ((shrug)) The other had only 3 out of 15 actually hatch, but he said at least 7 candled fertile (first time hatcher using a first time broody.)
The other good thing about shipping via Priority is that the boxes are free, and you can get tape from your local PO, and even order supplies free online from the USPS dot com website, which they deliver right to your door! I use the Priority labels to tape up my eggs, so the only thing I actually buy is the paper towel and the bubble wrap (I recycle all the macaronis I get in.)
At some point I'll do a video or take some pics of my packing process...