What training is required of an ESA:
The short answer is none.
The law defines an emotional support animal as "an animal that does not require training to do work, perform tasks, provide assistance, or provide therapeutic emotional support by virtue of its presence which alleviates one or more identified symptoms or effects of a person's disability."
Because ESAs require no training, they are not protected by the same laws as Service Animals. Thus they are not usually allowed in places that don't normally allow pets and can be asked to leave any establishment without cause.
See When is it okay to reject an ESA from an establishment
The only laws that protect ESAs are the Fair Housing Act and the Air Carrier Access Act (and loosely the EEOC). None allow you to bring your ESA into places that don't usually allow pets (example: grocery stores)
See What laws protect ESAs
Keep in mind, even in context with the laws that protect ESAs; tenants and airline workers are allowed to deny ESAs that are considered dangerous, causing a nuisance, or are destructive.
Because of this, despite ESAs not requiring any training; I still highly recommend it.
Only Service Animals have Public Access Rights. However, they must follow these guidelines. Although an ESA is not required to learn these, it may be in your best interest to train them as such anyway.
1). They should not show aggressive behaviors towards people or other animals when in public.
2). They should not solicit food or petting from other people.
3). They should walk calmly on a leash and stay focused on the handler.
4). They should not urinate or defecate indoors.
5). They should not sniff merchandise or people or intrude into other people’s space.
6). They should not vocalize or bark in public places.
