Human interest in communication with animals (and perhaps also true for vice versa) has been around for a long time. E.g. parrots, Koko the Gorilla, and Washdoe the Chimpanzee.
Communication is not just limited to the hearing domain but also the visual domain of languages. A pet can understand words in signed language as much as spoken language.
Humans and animals use different articulators of their bodies to communicate. Hearing humans use ears, vocal chord, etc. Deaf humans use hands, faces, etc. Animals use various parts of what they can communicate with.
Dog owners commonly talk with their dogs. Canadian psychologist Stanley Coren explains that the canines "can understand 160-200 words, signs and signals, and produce about a quarter of those gestures themselves." (Edmonton Journal, June 21, 2002).
Congenital deafness is not uncommon among pure-bred dogs, such as Dalmatians, Collies, and some Terriers. Eventually from birth, deaf dogs rely on eyes, nose and vibration to "hear".
Naturally, deaf dogs use visual cues that they respond to, just the same way as hearing dogs react to sounds. The visual cues that deaf dogs react to can be vibration, moving shadow, light, flashlight, and other peripheral movements.
You can train your deaf dog to pay attention to you when you call them. There are some different ways and possibilities to get your dog's attention: