Dogs shiver for a variety of reasons.
First and the most obvious to most people is the fact that they are indeed cold. Shivering contracts the muscles to stimulate heat.
The next two are medical and behavior issues.
Trembling and shivering are also indicators that a dog is in pain. If your dog is shivering on a constant basis you should rule out any medical conditions. You need to give him a complete body check to see if he has any sensitive or painful areas. Touch his whole body gently and carefully. Run your fingers down his back and legs gently, check under his tail. Check between his toes and check the pads of his feet. Look at his face, cup it in your hands and slide your hands down his chest. Check his eyes, ears, and mouth. Look on his belly and rub it gently. Even if he does not appear to be sensitive to your physical touch, there are still many metabolic problems that could cause pain. Make sure he is medically cleared by your veterinarian before assuming that the shivering is not medically based. (Especially if you notice anything else abnormal--not eating, listless, vomiting, diarrhea, limping, reluctant to run or jump, etc.)
Good signs that the shivering is behavior based is that it is NOT constant. Hhe doesn't shake when he is eating, playing, interested in his walks or "gets to go for a ride," etc. Shivering can be a symptom of stress, separation anxiety, and or fear. See this site for more info:
Dogs can also use shivering as an attention getting behavior. Remember, dogs will repeat a behavior that gets a positive response. That's the whole premise of positive rewarded--based dog training. So just like sitting politely (dog's behavior) brings forth a cookie (positive reinforcement), some dogs have found that shivering (dog's behavior) brings forth mom's concern in the form of attention (positive reinforcement.)
If you think this may be the problem you will need to determine what initiates this behavior and how you may be unconsciously rewarding the behavior. For example-- if he only starts to shiver when you start to leave the house and you notice the shivering and come back to pet him and "reassure him that its ok" then you are rewarding the shivering behavior. As long as the shivering is rewarded the behavior will continue! To extinguish this behavior you will need to start ignoring the shivering and reward him and pay attention to him when he is NOT shivering. You can also try distraction by playing games with him working and reinforcing his basic obedience skills. Remember NO positive reinforcement when he is shivering!
In short, make sure there are no medical reasons for his shivering and if not, then address the behavior issues. You also might find it helpful to enlist a good trainer to help you with her behavior issues if needed. Just make sure the trainer is a positive, reward based trainer!
I hope this helps!!