Dogs often fear anything they haven't been exposed to by the time they are 14 weeks old. If this includes a leash and harness, your dog may even be afraid when you bring them out for a walk, something most dogs love. This may seem like a huge problem, but with patience, you can teach your dog to love the harness and become excited each time it sees the harness.
Training harnesses can be very comforting for fearful dogs once they are used to the feel of the harness. Harnesses wrap the body, which can provide comfort to dogs, as opposed to collars, which have a negative association to many dogs who have been abused by their collar. In addition, it's more difficult for dogs to escape a harness if they encounter something scary on a walk, providing safety.
Pavlov made classical conditioning famous in his behavioral experiment where he rang a bell before feeding dogs. By the end of the experiment, dogs would salivate when hearing the bell even if he didn't bring food out because they had developed as association between the bell and the food. You want to develop this same association between your training harness and your dog. Use your dog's absolute favorite treats. At first, give your dog the treats for simply sniffing the harness. Don't even try to put it on until your dog is excited each time it sees the harness.
Desensitization is often used in conjunction with classical conditioning, because in order for the conditioning to be successful, you must move slowly enough that the harness doesn't cause fear in your dog. Thus, first treat only for sniffing the harness. Then, slip it quickly over your dog's head and remove it immediately, giving rewards the entire time. Slowly build up to putting the harness on and fastening it. If your dog becomes afraid at any point, or refuses to take treats, you're moving too fast.
Once your dog is comfortable with the harness, additional training can begin. Allow your dog to wear the harness around the house, dragging a 6-foot leash. Begin leaving the house once your dog is comfortable with the equipment. If your dog is afraid to go outdoors, this must be done slowly as well. Use treats to lure your dog to the front yard. Sit in the front yard for a short time, petting your dog, and then reward calm behavior by returning to the house. Build up to walking to more challenging environments.
Don't use punishments with fearful dogs. Dogs who are growling or snapping out of fear should not be punished, because that will make them even more fearful. If your dog is struggling, move more slowly or use better treats. Keep training sessions short to avoid stressing your dog. As your dog learns to trust you, its fear will lessen, and it will handle it more easily.