Dogs are predators, so naturally, we figure they would be pretty motivated to go after small prey, including mice. This may or may not be the case, however. A domesticated dog, without a particularly strong prey drive and no socialization with other dogs exhibiting a prey drive, may not be that interested in catching mice. So if you have pesky little rodents in your house you may have to train your dog to catch mice.
Some dogs, such as terriers and Dachshunds have been bred to go after small prey and take to mice catching quite handily. Other hunting breeds may also not need much encouragement to hunt mice. However, if your dog is not naturally inclined to hunt mice, you may need to give him some exposure, guidance, and make a fun game out of tracking and earning rewards for locating and catching mice. Then mice catching can be part of your dog's job, and dogs love to have a job.
Dogs have very acute hearing, much more than ours, so your dog will locate mice either by the sound of their activity or by their scent--dogs, of course, have very powerful senses of smell, and love to follow their nose. Engaging your dog's senses, especially his sense of smell, is a great way to get him turned on to catching mice. Young dogs may think catching mice is more of a game, and although they may be interested in catching mice, their ability to do so and what to do with a captured rodent may elude them. Working with a young dog to encourage them to hunt mice and practice catching them will develop the skills they need to catch mice as they mature.
You can purchase pet mice from a pet store, capture wild mice in live traps, or purchase commercially available mouse scent to aid you in training your dog to catch mice. Never punish your dog for not catching a mouse, as this is only confusing to him and will create a negative association with mouse hunting. You may want to take precautions to prevent pet mice from being harmed during the training process, such as using a cage or providing them with escape routes. Using food as a reward and a positive association with mouse scenting is useful to motivate your dog and let him know when he is on the right track to catching a mouse.