I currently own four deaf and blind Great Danes – Ice, Zero, Salt & Summit and we are also a Rescue that focuses on the special needs that includes those that are deaf and/or blind and we can have any number of deafies etc. with us at any given time.
My biggest piece of feedback when it comes to owning a deaf dog; is that one CANNOT be lazy. You cannot just `call out` to ask your dog to get their nose out of the garbage or to put that shoe down that they are walking off with. That is why it is so important to teach them the `watch me` or ‘look at me’ command. I even have used a squirt bottle to ‘alert’ to get their attention during training times with some dogs. I have also used a gentle finger on the rump or under the chin to get them to take the focus off what is they are doing and to look at me. I will point at the ‘garbage’ for example and then use the ‘dogs name’ and then the ‘No’ command and then re-direct to an appropriate thing for them to be doing.
I train my dogs as individuals, in pairs and in small groups to maximize their training and bonding experiences with me. Lots of body language plus facial expression really assists with in training a deafie. AND I also talk to my deafies all the time. My special needs Danes love to cuddle with me and just ‘feel’ the vibrations as I talk to him.
I can honestly say that our deafies often ‘listen’ better than many hearing dogs I know. 
I teach all our hearing dogs the same thing for I believe it to be equally as important for them too(and many will lose quality of hearing and eyes sight as they age as is) and use a combination of ASL and made up hand signals. One has to be very consistent about the signal they are using to associate ‘what’ command to ‘what’ action is being requested. I use touch training, light training(flicking lights on and off when they are outside in the fenced in yard at night for example), scent training and vibration training(we do not do vibration or shock collars here) but use our floors and door jambs.
At one time, I greatly immersed myself in ‘clicker’ training with deafies yet, I am still out on the jury on this one at this time.
I also teach a regular course that is specifically designed for owners and their deaf and/or blind dogs.
The one other thing I have found in relation to deaf dogs is that many do not feel it necessary to ‘name’ them. I am not sure why people feel that a ‘deaf’ dog does not need a need a name, because they are deaf. To me, that is like saying, we should not name our deaf children or address our hard of hearing or deaf elders anymore by name etc. A name is an identity and if one is living in a home with multi dogs; especially deaf one’s(we live with 8 at the present between our own and the Rescue); using a dog’s name is very important. If I am doing recall training in my almost 3+ acre fenced in yard; if I want X or Y to come to me, I use their ‘names’. If I want Y or X ; I signal their name. I am not in agreement with those that say that it is not important to name your deaf dog. Their names are no less important to them or to me. When I signal X’s name, their tail wags and the same applies to Y and each knows when I am `speaking` to them over the other or if I am communicating to both or more at the same time. They are proud of their own identities and how it makes them feel unique and special just as each hearing dog feels unique and special with their own names. To me, it is also a huge safety thing in regards to teaching emergency stops, recalls etc. They learn their names as much as they learn the `watch me` or ‘check in’ command; right from the get go.
I also highly recommend working on the ‘startle’ reflex while they are sleeping or napping.
One more thing to note is that many Special Needs will ‘stare’ at other dogs as they try to figure out what is being communicated. They are not doing this to be confrontational. As they are deaf/hearing impaired and/or are limited in sight; they will rely more heavily on other senses and can often be seen really looking at other dogs without any ill intent whatsoever. I liken it to how us Canadians would call a ‘stare’ in Canada is no more than a ‘glance’ in Europe. Many dogs can and do take some exception to this and you have to be careful that nothing escalates.
Deaf dogs will also often get really ‘up’ into another dogs’ face in order to understand what the other dog is ‘communicating’ or is like. Many dogs can and do take offense at this when none is being given and so you have to be careful to ensure that your special needs dog is safe from harm. They are only trying to read the other dog with their other senses. Many deaf dogs also have some form of visual impairment. Could be minor, could be major. Another reason why they get close up to other dogs and people too just to make sense of what is around them.
I teach everything from:
Their Name – I use the first letter of ASL of their name
Watch Me and Check In – I use a toy or a treat to begin and have them follow it to my face – general eye/nose area to look at me and reward – this changes to praise only through time where I then use just two fingers index and middle, slightly bent. I want them looking at me, not looking for the treat. I do not ask them to ‘look’ me in the eye. Behaviourally many dogs are not comfortable doing this and they will look at me from the corner of their eye or have eyes slightly averted yet they are watching me and I can see when I avert my own eyes a bit, that they will look more fully at me. There is a difference between having them look and watch you and having them stare at you. Dogs that have self-esteem issues and confidence plus trust issues, do not feel 100% comfortable, at least at the beginning to understand that it is ok to look at me at me eyes and that I am not asking them to stare or seeking conflict.
Off – Finger pointing off for example, the furniture
Up – Finger pointing up
No – ASL sign for no or shake finger sideways a couple of times and can include head shaking in a ‘no’ manner
Lay Down – Finger pointed towards floor or touch the floor/ground
Shhhhhhhhhhh – Finger to the mouth with lips
Quiet – Pretty much like SHHHH
Enough – One palm flat and the other hand makes a firm chopping motion up and down a couple of times
Get out of there – the thumb and hand position of someone hitchhiking, tilted on a slight angle and wiggled a few times
Now – One finger firmly pointing down right in front of me
Come – Waving motion towards me and can be one hand or both
Sit – I use one hand, two fingers curled down and motion up and down a couple of times
Stay or Wait – One finger pointed at them and then flat palm facing them for a second or two
Heel – point to my heel
Close – two fingers pointed down by my side
Kiss – make a kissing face with lips
Good – Big smile, clapping, head nodding up and down or thumbs up and variations on this with how ‘good’ they have been! I have even jumped up and down I wanted them to know how happy I was.
Yes – Same as above
Boy – ASL sign
Girl – ASL sign
In – Four fingers bent motion wave towards the direction I want – as ‘in the car’
Out – Same thing with motion to come out
Eat or Meal Time – Slightly open mouth and motion either with or without treat towards mouth
Gentle – ASL sign for gentle
Whoa/Easy – One hand palm out towards them and slow back and forth a couple of times motion
Thank you – ASL sign
Check Back with me – I motion them over during training and social times and when they come, I do a palms up, then a thumbs up and a double pat to their sides or chest as praise and sometimes also reward with a treat….through time, though it starts off as a ‘fun’ game for them, they learn to quickly come back and often to ‘check with me.’
Go There – Point at where I want them to go such as when we have visitors and I want them to lay on their dog beds until people get settled
Release or Go Play – Both hands motioning outwards from my body on an angle
Bed time or what we call sleepie time – hands placed together on one side of head and resting
With each command, I use their ‘name’ sign and the command as much as possible. I tend to try and use many signals that require only one hand use for I am often holding something in the other hand – treats, toys, their leash, bag, tote, purse, more than one dog, etc.
They know quite a few more signs too and what works for one dog might not work best for another, so being resourceful is important….yet, I have written a HUGE Gwennie novel! 
It never ceases to amaze me when people learn that any of our dogs or those in our Rescue program are SN’s. So many get this ‘pity’ or ‘sorry’ look on their faces and think I am doing them a disservice keeping them alive or they think the dogs are dumb or stupid…which could not be further from the truth. Two of mine are also Certified Therapy Dogs. Education and awareness has been key in communicating to a lot of people. Yet, with anything in the world, there are idiots.
Deafies have been a weakness of mine for almost 30 years now and LOVE LOVE LOVE them!