General speaking, from a receiver of many fish from the mail,basically, find the most direct flight. Then get an insulated box, a box with styrofoam lining. I've received fed-ex boxes with styrofoam lining on all sides, simple. Then if possible bring the animal to the airport, if not, box it as late as possible before pick up. Most use oxygen to fill the bag. Then double bag or even triple bag. Long flights, 5+ hours, some will drug the fish some how?
Just e-mail a importer (Wes from Rare Fish is a good guy and ships with some kind of calming drug, he may have some info?).
I would say Fed Ex is the way to go 99% of the time. Depending on where you live. They guarantee next day. If you can get FedEx "next day" you will be fine.