Common problem. Easy solution. Exercise, restriction and distraction. Ok, maybe not so easy for every case of the "digs".
Some breeds dig for shelter or to cool off. A Husky is an expert digger. Labs are notoriously diggers. Most dogs dig out of boredom and excess energy. It is often dogs that are under-exercised that cause the biggest challenge when it comes to tearing up new holes in the yard week after week. Here are a few tips that work well when all integrated into a behavior modification program.
It is ideal to set a dog up for success and for many dogs that means not leaving them alone in the backyard and expecting them to just lay on the deck all day and ignore that natural tendancy to dog. If your dog digs, you should consider leaving him indoors in a safe, comfortable place. Whether leaving the dog inside or not, it is important to get exercise before the long (all day for many dogs and owners) and boring separation. A jog, swim, trip to the park, brish walk or game of fetch should become a daily ritual. It's part of owning a dog that has enough energy to dog up the yard. Follow this up by leaving the dog inside for a few days or weeks. When leaving for short periods of time (15 minutes -1 hour) try leaving the dog in the yard and praising good behavior upon return.
Be sure to provide distrations for the dog such as favorite toys, a deck where they can see people or other things going on, or cement or wood areas where they can be away from the tempting dirt and grass.
Catching a dog digging can be a good time for a stern "no". Follow up this correction by immediately removing the dog from the area. If you have a place (field) where the dog is allowed to dig, then use this opportunity to encourage digging, but never at home!
Finally, be sure your dog is well integrated into the family. Dogs that are part of a close knit family have few behavior problems and when they do, are ideal students for a modification program. Try to find time for the dog to be with the family in and out of doors.