I'll elaborate a bit more...
You and the seller will confirm a shipping date. On, or maybe even before that date, the seller will email/text/call and give you a waybill (tracking) number. They may also give you the flight number with an expected arrival time of the flight they plan to ship on as well. Check the waybill number frequently throughout the day though. The estimated time of arrival can vary from the actual time of arrival by a bit due to delays or sometimes faster flight times. As I stated before, once they've arrived you simply give them your shipping info, show them your I.D., pay for the shipping....and drive home excitedly with your fish.
If there is a problem with your fish such as a d.o.a., you usually need to take a picture or two and send them to the seller within an hour or two. Usually it goes very well with air cargo though, I send and receive shipments through air cargo quite frequently and it's definitely the safest way of shipping i.m.o.