I traveled several times with my tiny minpin and once with my Rhodesian Ridgeback to Nicaragua.
I had to get a health certificate and shot record authenticated by the FDA, I believe. The exact process required is published online. It was no big deal to get the seal. I just showed up with a stamped health certificate and they stamped it after verifying my vet's stamp.
Once I got to Nicaragua, it was no big deal. You just present the papers and then pay a "visa" for them to enter the country. The process takes like 15-30 min.
Getting them back into the US was just as easy. There was no problem once we arrived back home. Customs just wanted to see the original health certificate and the new one, proving they originated from the US and were just coming back home.