There is really no set dog sign language. You can invent any hand signals for training deaf dogs that you like, that is to say, that you can do naturally and consistently. Your dog will be reading your body and hands exclusively, so hand signals don’t have to be official “sign language” as standardized for use by people who are deaf. Just ensure whatever signs you decide to use for training, everyone involved in the regime uses the same training hand signals consistently so you don’t confuse your dog.
It’s also a great idea to document your shared hand signals for deaf dogs by way of photographs for any temporary caregivers.
Training deaf dogs is much the same as training a hearing dog. You lure the dog into the position you want, say and sign the command at the same time then reinforce that with a treat and lots of praise. Lots of owners of deaf dogs, including myself, still talk to their deaf dogs as it just feels like a natural thing to do. I also believe that dogs may be able to read our facial expressions and they can definitely read our body language when we talk with the signs. When people joke that I talk to my deaf dog, I tell them that he reads lips and wait to see how long it takes for them to realize I’m kidding!
Deaf dog hand signals courtesy of The Deaf Dog Network