It depends on where they are going, how many eggs are in the box, what type of box you use, and how you pack them.
I've been mostly sending out quail eggs this summer, all my chickens are broody it seems. For up to 40 button quail eggs (like I ever have that many!) or up to 20 coturnix eggs it's usually $5 for shipping with free DC# through online ship and click.
I would say the average cost of shipping I've paid would be $7 or $8, but there are some that have been as much as $15, though not many.