There are 2 schools of thought on this subject. One is to either confront the dog owner yourself or have animal control dept do it. Try to get them to pay for the damage, etc. The problem with this approach is that some people just don't think their dogs did it (where's your proof?), or don't care because, after all, you can buy a chicken at
Walmart for a few dollars, so no big deal. Their dogs are wonderful, never cause any trouble, etc. Then there are other people who will try to get even with you for causing them trouble. Some people will do the right thing and pay you for the damage, and keep their dogs home in the future. You won't know which kind of person your are dealing with until you try it.
The other school of thought is the three S-es, shoot, shovel, and shut up. This eliminates the dog problem, but if the owner knows you shot his dog, he may try to cause you trouble.
The best solution to the problem is to avoid it in the first place. The only way to do that is to build a formidable fortress for your chickens, and other critters, that dogs can't tear into. I've tried to do that and so far haven't lost any more chickens to dogs or coyotes. Hawks and owls are a different matter tho.