Getting Your Pet Through Customs
After the airline, your next stop will be with the host country's customs office. They'll have their own ideas about all of the above, as well as they key issue of whether or not they will admit your pet at all. To avoid the spread of certain diseases, all countries limit what types of animals can enter. Many will only allow a pet “in” after a length (and you pay for it) quarantine in the host country. All of this will take time and cost money. Start with the host country's Embassy or Consulate in the U.S.
Many countries will require a Certification of Veterinarian's Examination Statement. This is available from most vets.
If your vet is not properly accredited to issue such a statement, you'll have to either locate a vet who can help you, or submit your unaccredited vet's statement to the Department of Agriculture's Animal and Plant Health Inspection Service (USDA, APHIS) or call 800-545-USDA. Allow plenty of time.
Lastly, when it is time to come home to the U.S., our own customs and agriculture people will have their own ideas about when and how to admit an animal that has been abroad, fearing again the importation of disease.
U.S. Customs has a good publication on pets.
The U.S. Department of Agriculture's Animal and Plant Health Inspection Service (USDA, APHIS) also has a page dedicated to resources regarding pets.