Long story short, they will remain viable for a week to 10 days.
The longer they remain out of the incubator, though, the less chance they have. 10 days is the "official" limit. You want to ensure they are shipped within 24 hours of being collected.
They are normally shipped 2-3 days priority, but you can have them express shipped if you want to pay for it.
Now shipping does take its toll on fertile eggs. All the knocking around and harsh handling is not good for the fertile germ. Don't get me wrong, it is still a good way to go. But there are some risks from the shipping process and sometimes eggs are either damaged or rendered infertile.
On the other hand, shippers with even a little experience pack securely and do well. I recently got some shipped eggs with not a one broken. I'll soon see if they hatch....