The size of the dog run depends on the size of the dog or number of dogs and also the amount of space you have. For a small dog, the size should at least be 4 ft by 8 ft.
There are different types of dog runs e.g. a dog run with grass, a concrete dog run, a run with wood chips or a gravel run (if using gravel make sure it is not the sharp kind or you could end up with a dog that has cut paws).
If the dog run is on grass, it might not last long in that area. Dogs tend to tear up grass and, in the winter, can destroy it, simply by playing on it. A good solution is to put down wood chips to cover the mud and keep your dog’s paws clean.
The fence should be between 3ft and 8 ft high. Check what the specified dog breed is capable of jumping over. You do not want to go to all the effort of building a fence, only to find out later that it is one foot short.