If the animal is breathing but unresponsive, you will want to try to keep its airway open. Remember to take your own safety into consideration, as a lot of dogs will bite when in extreme pain.
Control any bleeding with compression. Apply hand pressure with dry gauze over the wound if you have it. You can seal the gunshot wound with plastic of any variety to keep air from being sucked into the wound. Don’t give the dog anything to eat or drink. If you can get a veterinarian to come to you, do so. If not, carefully bring your dog into a vehicle in which they can be kept as flat and stationary as possible. Use a board, preferably, or a towel or blanket stretched taut.
The damage may look more serious than it is, but life-threatening conditions can also look deceptively innocuous. Do not delay in getting the animal to a veterinarian.