Timing is the most important. You should start at least 6 months in advance. Now, if you do not know where - or even IF - you are going outside of the country, as was the case with us, you are already behind because regulations differ from country to country. We assumed that eventually we might possibly want or need to bring Pepper to her grandparents in England, which is like the worst case European scenario for transporting animals. England does not have rabies in the country so Pepper needed an expensive rabies titer test and subsequent paper work. Oh, and hopefully, all of this was preceded by implanting a microchip of the appropriate standard - bet you didn't know there were multiple kinds? or that getting your microchip company to tell you which one you have is its own exercise in patience?
Even booking the travel requires the flight has room (usually only 1-2 spots) , is not during a weather embargo (so your dog does not roast or freeze), has a short total itinerary (since you won't get to see them again until the final destination), and each layover destination does not have its own restriction (dogs need a minimum of 6 hours for transfer at London Heathrow). Each airline has its own documentation as well.
Then there was the final check-up. Eight to ten days in advance Pepper went for her final exam with the vet in Indiana to get 2 forms filled out - one for the USDA (required by the airline) and one for the EU (with directions in Spanish and English). After the quick exam, I was suspicious at how long the vet's office was taking to fill out the only 3 pages of forms. I nearly ran out screaming when the vet tech said, "Oh, is Spain in Europe? I thought it was somewhere in South America." ... Really should I have been surprised to hear from the USDA that the examining vet's office mucked up the entire thing? The USDA blasted them for not even being able to consistently write the dates in the same format (dd-mm-yyyy vs. mm-dd-yyyy) on the same page! Another trip to the examining vet to pick up the "corrected" forms revealed glaring discrepancies even I could see, like an error in Pepper's microchip number. The full extent of the their complete incompetence was exhibited when it took three (!) revisions of the corrected forms - each one printed and stamped - to finally catch all the mistakes.
The appointment to hand deliver the forms to the USDA had its own hiccup. A quick call to our vet in North Carolina and fax back were all that were needed to get the precious embossed certificates.
The actual trip, by comparison, was uneventful. Pepper got to walk around with me until 2 hours before the flight out of Chicago. She learned how to drink out of her new guinea pig-style water bottle. I was nervous because I was not able to see her crate loaded on the flight out, but someone in Zurich checked on her for me. In Barcelona, an airline employee assisted me in wheeling her out, straight past customs in the "Nothing to Declare" line, and no one stopped us. After all the drama of getting her paper work, this did not seem right to me. However, despite repeated attempts to ask at Information and Security, they assured me that it was okay and they probably checked her paper work in Zurich. I find this fishy since the airline only took the USDA certificate, and no one saw or asked for the EU form - but I'll take it!
Our darling girl was none the worse for her 15 hour journey, other than being a little ashamed at wetting the crate. Later on Richard and I found that Pepper also was jet-lagged, excitedly wanting a walk at 4 am, which we thought was hilarious! I keep telling her she needs to not sleep so much if she wants to adjust.
One final note for detractors: We did make a conscious effort to include Pepper's welfare and well-being in our decision to move to Barcelona. Richard and I felt the relatively short-term difficulties of getting her into Spain will be far outweighed by our next 3 years here. Dumping her back in the shelter (unthinkable) or even with our parents would have been irresponsible ownership, and we are a family. She goes for long walks everyday and has already been to a couple of dog parks.