Create a do-it-yourself live mouse trap. Place a large, tall glass jar, bucket, or trash can somewhere along the path that the mice normally take (typically along the way to a food source). Put cereal grains, nuts, or other tasty bait in the jar and make a little ramp up to the jar (something like a paint stir stick or scrap piece of wood works nicely). The mice will climb the ramp to get the food, fall into the jar and be unable to climb back out again.
Make sure to check the trap regularly, preferably at least every couple of hours - it is distressing for any animal to be caught in a trap and they could easily die from the stress or dehydration.
Try an ultrasonic repellent device. These devices emit noise or vibrations that mice don't like (but people can't hear), encouraging them to leave. There have been mixed results with the use of these devices, with some people swearing by them and others emphatically stating that they don't work. Mice can get accustomed to these devices so if they work, they tend to work on a short-term basis. There are many types around and you may need to try several. Look for one that changes patterns to try to prevent mice from getting used to them too soon.
Note that some people report that they believe their pets can hear these devices. Pets have much better hearing than humans, so it's entirely possible that ultrasonic devices can be irritating or distressing to pets.
IF YOU DO *NOT* HAVE CATS - try peppermint oil. Mice reputedly hate the smell of peppermint and will leave the area on their own. Drip some oil onto cotton balls and place them where the 'mouse attractants' are, such as nesting areas and food sources. This will encourage them to go elsewhere. Do not place peppermint by the entry holes if the mice are already in the house since it will encourage them to stay inside rather than get rid of them.
Do not use peppermint oil if you have cats! Cats are very sensitive to this oil and can become very ill.
Many dogs and cats themselves are great at controlling mice. They don't even necessarily have to catch them - in some cases, their presence and scent is enough to keep mice away. If they do catch them (and some dogs are better mousers than cats!), be sure to tell your veterinarian, who may advise that your pet be dewormed since mice carry parasites.
Do not use snap traps or poisoned baits. There is a risk that your pet could end up caught in the trap (even a large dog can catch a paw in a snap trap), or find and ingest enough of the bait to make him sick or even die. Dogs can nose their way into areas they shouldn't go, especially when they smell something interesting. And cats are masters at getting into small or hard-to-reach places! Even humane live traps should be carefully checked and considered - can your pet's head, face, snout, or paws get stuck in the trap if they were to attempt to reach the bait? Glue traps are also not recommended. Aside from being inhumane to the mouse and other rodents, pets can get their paws stuck to them and glue traps can be difficult to remove.
Some professional pest control services specialize in "pet-friendly" pest removal and control. If this is the route you take, ask to see safety information on the chemical they propose to use in your home.
These pet safe mouse control methods are also humane pest control methods that minimize the risk of stress or injury to the mouse. Figuring out how to get rid of house mice is just one step of the process - after they are gone, homeowners should turn their attention towards preventive pest control to try to stop mice from returning. Remove access to the things they want - namely warmth, shelter, and food - or make it uncomfortable for them, and you're one step closer to being mouse-free.