There are three particular acts to be familiar with that help govern and protect you and your Emotional Support Animal.

Americans with Disabilities Act: The Americans with Disabilities Act addresses Service Animals, which is different from Emotional Support Animals.
Fair Housing Act: Your Emotional Support Animal is protected under the Fair Housing Act, which prevents you and your pet from being discriminated against.
Air Carrier Access Act: With an emotional support animal you and your pet are protected from discrimination by a commercial airline. This act allows your Emotional Support Animal in the cabin of the aircraft with you at no cost, even if the airline normally does not allow for an animal.