Whatever they say about not being able to teach an old dog new tricks, it is patently untrue. Old dogs may not learn as quickly as they did when they were young, but with time and patience, most older dogs can be taught to do anything that a young dog can.
Maybe the adage about age and learning was intended to be interpreted less literally. It certainly is true that dogs' personalities don't change much after puppyhood. Anxious or fearful dogs tend to remain that way. It's hard to persuade them otherwise. And you can't make a dominant dog super-submissive.
What you can do is teach such dogs how to behave in a particular situation, how to remain calm in a threatening situation and whom to look up to and respect as a leader. If a dog's personality is a hunk of wood, learning is a veneer superimposed upon it. Is the wood mutable? No! Can the veneer be changed? You bet - and at any age.
Teaching One Word Commands
Teaching the correct response to voice cues or hand signals is as fundamental to communicating with a dog as the alphabet is to language. Consistency is the key.
First, reward the dog for performing a desired behavior when that behavior occurs naturally. For example, give your dog a food treat for sitting, lying down or stopping barking. Initially, the reward should be selected to be practically irresistible, not just kibble or a piece of dry dog biscuit. The frequency of his performing the behavior will increase if the reward is appreciated.
Next add a word cue or sign that must preface the behavior if it is to be rewarded. This is called a conditional stimulus; it must be present if a reward for performing the behavior is forthcoming. The word cue, or other cue, should be delivered once and once only. If the dog is slightly deaf, speak louder. Whatever you do don't repeat the command. If the dog obeys, he must be rewarded immediately. If he does not, there is no reward. The opposite of reward is not punishment -it is no reward.
Using the above method, any behavior, even closing cupboard doors or fetching the newspaper can be trained - though more complicated behaviors have to be trained in stages ("shaped"). A clicker can be used to help people and dogs appreciate that they are in 'training mode,' and will help improve the timing of reward. (See Clicker Training Your Dog.) Punishment based techniques are unacceptable, especially for older dogs.
Even canine senior citizens will learn fairly rapidly using the above techniques. Obedient responses to commands, though intrinsically valuable as a means of increasing mutual understanding between owner and dog, may also be employed to help resolve behavior problems. For example, dogs that are barking too much, and at the wrong times, can be trained to be quiet on cue. House soiling dogs can be rewarded for 'going' in the desired location outside. And dogs with separation anxiety can be trained to spend time at a distance from their owners (independence training).
On the lighter side, genuine (party) tricks, like "bang" (you're dead) and the dog rolls onto his back can be taught, even to old timers. The very act of spending time with the dog, plus the sense of accomplishment and communication that training brings, is well worth the effort and improves the quality of an owner's and pet's life.
If you make sure that your aging dog is always learning, always occupied and always has something new to busy himself with, he will probably be more likely to stay bright, alert and mentally active for a long time, perhaps well into old age. Being constantly subjected to an interesting and stimulating milieu may increase your dog's lifespan and health span. Never mind, "you can't teach an old dog new tricks." I prefer, "if you don't use it, you lose it." Keep thinking about this philosophy and keep training your dog - right to the very end of the road. Neither you or your dog are too old to learn.