Assuming you aren't driving and therefore can't place them in a bucket with an air source, the best bet is to ship them in breathable bags.
The most widely-known breathable bags are Kordon Breathing Bags:
- Stocked sizes include:
- 5.5" x 8"
- 7.5" x 12"
- 11.5" x 19"
- Breathing Bags allow the transfer of carbon dioxide and oxygen through the plastic wall of the bag.
- Carbon dioxide exits the bags at 4 times the rate oxygen enters the bags, thereby constantly purging the water of toxic carbon dioxide.
With no need for an air space shippers can fill the entire bag full of water. This in turn provides more room for the occupants and also prevents stressful sloshing that occurs in transport. An unlimited source of atmospheric oxygen allows shippers to choose slower and more economical methods of transport.
One major key for shipping, in my experience, is to fast your fish for an appropriate amount of time prior to shipping. This allows their metabolism to slow a bit, but more importantly, it purges waste from their bodies prior to moving them into the shipping bags. The less waste they produce during shipping, the less ammonia will be present in the bag. Normally a 3 day fast period is best, but depending on the fish and the size of the fish, more or less may be appropriate.
I also believe in moving the fish into a separate container prior to shipping for them to purge their bodies of the last waste. Usually a move will "shock" them into doing this. Then, move them into the shipping bag with clean water.
You will also want to keep them in the dark during transport. This will keep them calm and cause less stress.
Another key is to ship them in an insulated container that will keep them warm/cool depending on their conditions and the weather.
If your fish are healthy and shipped correctly, the chances of them surviving the trip are very high. Be sure to acclimate them properly in their new home to avoid shock!
Quick edit - it's best to leave one fish per bag, in case one doesn't make it, it won't cause water conditions to deteriorate for the others!
A note about pressure changes in air transit - This is a concern with regular bags that are filled with air, the change in pressure can affect the bag tension. With the breathing bags, the exchange of oxygen through the membrane paired with the fact that the bags are filled with water and no gas, allows the fish to be shipped with no concern in pressure change.