The Humane Society of the United States and the American Society for the Prevention of Cruelty to

The Humane Society of the United States and the American Society for the Prevention of Cruelty to Animals recommend that you do not transport your pet by air unless absolutely necessary. But if you must:
Check with your airline first before bringing your pet to the airport.
Many airlines allow small pets to be carried in the passenger cabin, but make sure your kennel fits under the seat.
Before your trip, take your pet to the veterinarian for a checkup and make sure vaccinations are up to date. Do not give your pet tranquilizers unless prescribed by a veterinarian.
Don't feed your pet four to six hours before departure.
Make sure your pet is wearing a collar and an ID tag with destination information in case it escapes.
Book a direct flight and take the same flight as your pet. Avoid travel during busy travel times; your pet is more likely to be roughly handled then.
Don't ship pug-nosed animals such as Pekingese or bulldogs in cargo holds because their short nasal passages make them vulnerable to oxygen deprivation and heat stroke.
Buy a shipping crate that's approved by the Agriculture Department and large enough for your pet to stand, sit and change positions comfortably.
Write "Live Animal" in big letters on the side and top of the crate. Draw arrows to show the upright position. On top of the crate, write the name, address and telephone number of the pet's destination, and who is picking up the animal.
Tape a photograph of the pet on top of the crate in case it escapes.
Line the crate bottom with bedding to absorb the impact from an accident.
Freeze your pet's water so it won't spill during loading but will melt by the time the pet is thirsty. Tape a small pouch, preferably of cloth, of dried food outside the crate.
Source: Associated Press