Hyperactivity is a common complaint among dog owners, especially those who own herding and sporting breeds. Dogs that are often accused of being hyperactive are actually dogs that have high energy and not enough outlets for that energy. In some breeds, such as setters, the original function of the dog required a high energy level. The average hunting setter will cover several miles in pursuit of feathered game, and a high energy level was selectively bred into the dog. When this same dog is kept in a suburban or urban environment, it typically has no outlet for that energy, often resulting in behavior that might be called exuberance or bounciness by those who appreciate the activity level or hyperactivity by those who do not. The best way to deal with a dog with high energy is to do as much as possible to find outlets for that energy. It is also a good idea to carefully consider the breed specific temperaments and characteristics of any breed of dog before bringing one into a house hold. Some dogs are too energetic to be happy in the city without extensive exercise.
The first dog I remember that was called hyperactive was a Dalmatian belonging to relatives who kept him in a suburban environment on an invisible fence. Dalmatians are derived from sporting dogs that are really similar to setters and pointers in energy level. This high energy was used in the Dalmatian to make them be able to travel with carriages and coaches during the eighteenth and nineteenth century. A Dalmatian that is not given enough exercise is going to be hyperactive, and this one was no exception. He was so bored with his life that he developed lick granuloma, a condition in which he licked until great sores appeared on his feet. It was clear that he was not happy in the suburbs, so he was sent to the rural farm where I grew up. There, he had room to run off leash and play with another dog, a golden retriever of a similar age and activity level (although he could always wear her out, and she was a very active dog!). He could relax after a long day's run in fields and forests, and he stopped licking sores on his feet.
This dog taught me that very active dogs merely need outlets for their energy in order to be happy. Most urban and suburban dwellers lack access to open fields and forests where a dog can run safely, so the only solution is to come up with ways to release that energy. Long walks on leash can help release that energy, but be aware that many of these dogs can go miles at a time at a very high speed. A very active dog can run faster and for longer than any human. Walks on the leash, then, must be extremely long and frequent during the day. One should look for dog parks and other areas for the dog to run off leash, but if this is not possible or if you are uncertain of your dog's temperament with strangers or other dogs, leash walking is going to have to be the main outlet to release that energy.
Dog agility and fly-ball might be good places to exercise the hyperactive dog. Dog agility in an obstacle course in which the dog must move through each obstacle quickly and under control. Dog agility can give the dog a workout, as well as increase the owner's control over the animals. It can also strengthen the bond between owner and pet. Fly ball involved the dog leaping down a set of jumps, hitting a box at the end of the course, which releases a tennis ball that must be caught in the dog's mouth, and then racing back down the jumps to deliver the ball. Many object obsessed dogs, like border collies and retrievers, can find this activity rewarding.
One can also do working trials. Gundogs and hounds can do hunting trials and working tests, which test the dog's ability to hunt game as it was originally bred to do. Herding dogs can do herding tests and trials. Dogs like German shepherds and Malinois can learn to do protection sports like Schutzhund and French ring, which are probably sports that the average dog owner should only do if they really understand dogs. In the urban environment and in the suburbs, one can find outlets for the active dog.
Clearly, an active dog can be an asset to the family. One just must find outlets for that energy. One should get the dog checked out by a veterinarian before engaging in any of these activities, because there may be a reason for the hyperactivity that are medical in nature. However, it more likely that the high energy level has something to do with the dog's original purpose. If that energy level is not met, then hyperactivity can be a result.
Finally, one really should consider the energy level of a particular dog or dog breed before bringing it into the city. Some dogs really need lots of exercise to be fulfilled, and in our busy society, it is very difficult to meet those needs. Some dogs are really laid back and mellow, and this can appear in different lines of the same breed. Working-type golden retrievers are far more active than show-type golden retrievers, especially those from European lines, i.e. "English cream." Make sure that the dog one chooses to live with really fits the energy level of the family and its time constraints