MY WAY:
You can go to the usps website and order boxes. I use the #4 and the #7 boxes the most. The #4 is good for 1-2 dozen quail eggs, 8-10 bantam eggs, or 6-8 standard eggs. The most I have sent in the #7 box is about 28 bantam eggs, but there was room for more
You can also get priority mail labels to use as tape for wrapping the eggs. Plus, they are all free, unless you get prepaid items.
The way I do it is to take small-bubble bubble wrap and wrap each egg individually. For bantam sized eggs you can wrap 4 with 1 12x12 sheet. I roll mine up from corner to corner, then tape the ends over. Then I take another sheet of bubble wrap and make an 'envelope' from it. The eggs go in this, as many as can comfortably fit. Bantams (all I have sorry!) can fit about 10-12 in one 'envelope'. Then I put crumpled or shredded paper in the bottom of the box, take a sheet of large-bubble bubble wrap and lay it on top of the paper, then place the eggs on top of that. If that is all you are sending, you take another sheet of large-bubble bubble wrap and lay that on top, then fill the box up with more crumpled or shredded paper. The key to shipping eggs is:
1) make sure the eggs don't bump anything;
2) do not let the eggs touch the side/top/bottom of the box
3) make sure there is enough padding (paper, pillow stuffing, packing peanuts) between the eggs and the box to absorb any direct hits
4) make sure the eggs are snug inside the box, but not too snug. You don't want them to get mushed in there! But you also don't want them to be able to move around at all.
5) don't ship them pointy side up. I usually lay mine on their sides.
6) mark the outside of the box as 'fragile' 'hatching eggs' whatever you want, as long as it is marked with something. Some people don't do this, but most people I have sent eggs to have had good hatches, so I don't think the p.o. is as rough with fragile packages as some others think.
You can also use an egg carton to ship in. I haven't had any luck with this, but a lot of eggs I have received have been done this way. Just wrap each egg with toilet paper, bubble wrap, paper towels, (you get the idea) enough so that they do not move inside the carton. A #7 or shoebox is good for shipping eggs in cartons. Then tape the carton shut, wrap the whole carton with bubble wrap and place in your 'padded' box.
Dipsey's way:
https://www.backyardchickens.com/web/viewblog.php?id=17-wrapping-packing-eggs
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