You’ll need to complete the paperwork through the particular airline you select.  Emotional Support Animals are very different from Service Dogs.  You will need your doctor to complete a form with a diagnosis as well as proper vaccinations for your pet.    Some airlines are requiring a psychologist or psychiatrist sign the letter, not your General Practioner. Your pet needs to be well behaved and trained.  There is generally no cost to bring your pet in the cabin but it must fit within the footprint of your seat.