Meet Pepper! When we relocated from Iowa, USA to Guanacaste, Costa Rica in 2014 she was 13. As I write this she's sniffing bird seeds off the ground and she's a strong 16 years old Shar-pei. We call her the best dog ever - which she most definitely is. We did discuss leaving her behind in Iowa, with family, but it was clear that wasn't a great option for her or for us. So off to the tropics she flew with us.
Forms were required. Luckily organization is my strong suit.
This is the link to the USDA form you will need to have endorsed by a vet:
You will need to bring it with your dog to the vet within 2 weeks of departure, then mail it to the USDA with a self addressed stamped envelope, so they can endorse it and send it back to you before your departure date. When we did this, it was admittedly a little tense but it all worked out fine. If you can drive to the USDA office, even better!
Please note that, in our experience anyway, not all vets are highly familiar with the paperwork you will be requesting. Familiarize yourself with it and make sure it is filled out properly so it will be notarized without issue by the USDA.
The overall summary from the US embassy San Jose on what is required can be found here:
Animals >3 years of age must be vaccinated for rabies
Endo/ectoparasite treatment is required between 30 days and 10 days before departure. (So just do this at the same time you have the vet fill out the USDA form above.)
Dogs have to have had vaccinations against distemper, hepatitis, parvovirus & leptospirosis. You will need to have documentary proof of these vaccinations from your vet. It won't hurt to make copies of every form, either, just to be safe. I vaguely remember copies being kept by airport officials. (Of course I was prepared. :)
Airlines have their own individual rules. Our dog, because of her size, flew cargo on our flight. We flew Delta. We paid $100 each way for her ticket. Her crate had to meet certain requirements that were available from Delta. She had to have food in a bag taped to the crate, a water bottle of a certain format (think like for rabbits -- that kind), and copies of the forms in an envelope also taped to her crate.
I am neurotic, and I did call ahead of time with all details to confirm we would be unhindered by surprises upon departure. We were with our dog at exit and with her again at entry. I recommend this, of course. You can hire pet agents (I can't remember what they are called), but honestly the process went so smoothly that I don't see why people should worry about doing that.
When it came time to fly from Costa Rica back to the States, we actually had to drive to San Jose and depart from there because it was too hot in Liberia and they will not allow dogs in cargo above certain thresholds of heat. It was not a big problem for us, as we hired our favorite driver, Macho (from Santa Rosa, Guanacaste) to enjoy the trip with us and say goodbye. Pepper was quite comfy in her large crate and we all made it back safely and with many priceless memories.