Hi, and welcome!
A PSD (psychiatric service dog) is no different from any other sort of service dog. Like all service dogs, they must be individually trained to do something for you that you cannot do for yourself because of your disability. Remember that, "[a]nimals whose sole function is to provide emotional support, comfort, therapy, companionship, therapeutic benefits, or to promote emotional well-being are not service animals." (U.S. Department of Justice)
Here's an article that explains more about PSDs:
http://servicedogcentral.org/content/node/74There is no legal registration or certification for public access in the US. You can purchase fake credentials over the internet, but they are meaningless because the dog is never even tested or evaluated in any way. Training typically takes 18-24 months, regardless of the nature of the disability if the dog is intended for public access use. Once that training is complete then the dog can be called a service dog and can wear a vest in public. The vest does not make a dog a service dog, its training does. Businesses are permitted to ask what the dog is trained to do and whether it is required because of your disability.
The only time PSDs are singled out from other service dogs is when flying on aircraft. In order to fly with a PSD (or ESA--emotional support animal) you must make your request of the airline at least 48 hours before your scheduled departure and produce documentation on demand from your treating physician that is no more than one year old and is typed on the doctor's letterhead.
Other than that one instance, a service dog is a service dog, regardless of the nature of the person's disability. All that matters legally is whether the owner is legally disabled and whether the dog is trained to perform tasks to mitigate that disability and to behave appropriately in public.