Make sure you and the dog meet the requirements for transporting across the country. The dog has to be at least eight weeks of age, and should not be exposed to temperature less than 45 degrees Fahrenheit. The puppy also needs a Health Certificate from a licensed Vet. If he is older than 16 weeks, he must have rabies shots.
Contact the airline you are traveling with via phone. If the dog is small enough to fit under the plane seat, you don't have to check him in rather you can take him as carry-on. For that, the fee ranges between $75 and $125, as of 2011.
If it's just the dog alone who is traveling, do some research on which airline would be the most economical solution for booking as checked baggage, for which the fee varies between $150 and $900 as of 2011, depending on the size of the dog. Some airlines that transport pets across the country include AirTran Airways, American Airlines, American TransAir, Continental Airlines and Delta Airlines. You can find the pet transformation information of each of these airlines in the Resources section of this article. You can contact the airline via helpline provided on the respective website.
Take the dog to the airport at least 24 hours before the departure, or as per airline's directions. When the dog arrives at the destination airport, he will be delivered at the Cargo facility within an hour or so. You can then pick him up and take him home.