The U.S. Department of Transportation regulations are different than those pertaining to the U.S. Department of Justice “Americans With Disabilities Act” regulations.
In summary, per the International Association of Assistance Dog Partners:
“There are new, more detailed procedures for the carriage of emotional support and psychiatric service animals. The carrier may require the passenger to provide current documentation from a mental health professional caring for the passenger that the passenger has a specific, recognized mental or emotional disability and that the passenger needs to be accompanied by the specific, emotional support of psychiatric service animal in question, either on the flight or at the passenger’s destination.”
“Foreign carriers are not required to carry service animals other than dogs.”
“If you are traveling with an emotional support or psychiatric service animal, you may be required by the airline to provide 48 hours’ advance notice.”
Naturally, contact your airline for their specific rules on service animals and seating. All service dogs will need a current health certificate as well. Most of the time, you won’t need to show it, but there may be a situation where it is required to board. Make sure you have it on you, not packed in your checked luggage.