Why does my dog fart?

It could be the food that's the problem. It's normal to pass gas, but if it's excessive you should take your dog to the vet to make sure it's not a medical problem. You can try feeding a high quality food that contains only one protein source and no grains. The protein should be one that s/he has not eaten before. Mix about 25% in the present food and gradually increase the amount of new food until that's all your dog is eating.