Pets in the Cabin
Pets are permitted in the cabin, but there are strict size limitations. For example, American Airlines says pets must be kept in a kennel that is no larger than 19 inches long by 13 inches wide by 9 inches high. Air France requires that the pet weigh no more than 8.8 pounds (4 kg) and fit in a kennel that is 45 linear inches (115 cm). Furthermore, every airline has strict limits on the number of pets they will allow in the passenger cabin, so it is imperative you notify the airline in question as far in advance as possible.
Avoid Connections
One thing you will quickly realize, if you study airline policies regarding checking a pet kennel as baggage, is that there is no uniform policy regarding how to ship pets. That means that if you are making connections through multiple airlines, your pet's circumstances must be in compliance with every separate set of regulations. It complicates matters to ship a pet using multiple airlines, and it should be avoided if at all possible. Furthermore, since your pet might not receive properly attention at all stages of the flight, you should seek to limit the time your pet will spend as checked baggage in general. Do your best to make the entire trip on one flight, even if it means using an airport that is farther away than usual.
International Travel
Be aware that importing a pet into a foreign country will require a trip to the vet and possibly a stint in quarantine as well. The requirements vary considerably, and should be researched at least three months prior to the date of any international travel. For example, the European Union is fairly relaxed and only requires a recent rabies shot (although this must be certified by the USDA) and an electronic identification tag. Americans seeking to take their dog or cat to the UK, on the other hand, will need to put their pet into quarantine for six months.
Avoid the Summer
If you are checking your pet as baggage, avoid traveling in the summer months. You should never assume that baggage handlers are going to do their jobs properly, so just imagine your dog being left on the tarmac in the 90 F sun with high humidity and no water for two hours before you plan to fly out of Atlanta with him in July.
Crate Train in Advance
The day of the trip is no time to be acquainting your pet with the kennel. The trip is going to be stressful enough as it is for your pet, even if it is in a kennel seated on your lap. If your pet is not already at least partially crate-trained, then it needs to be before your travel date.