It's possible, but you need to start the process as soon as possible to shorten or eliminate quarantine in some receiving countries.
Some broad guidelines:
International Pet Travel, Dog Cat Pet Quarantine, Importing Pets
There should be a vet in most metro areas of the country who has experience in dealing with any necessary vaccinations and paperwork.
It's common for pets to fly in the pressurized and climate controlled part of the cargo hold on long flights. Each airline has requirements on pet enclosure requirements for those flights, and many airlines will not fly pets in summer hear or winter cold because of concerns about them spending too much time on the tarmac in harsh weather conditions while they're waiting to be loaded.