Mice are very intelligent creatures.
Although rats are more often trained than mice (simply because they are easier to train and can perform a wider variety of tasks), a well trained mouse can be very impressive. Anyone who has seen movies like The Green Milecan attest to the kinds of tricks these little fellows can learn. The basic principle for training all animals apply to mice, but here are some specific ideas you can use.
Before you can teach him or her anything, you need to get your mouse accustomed to you and win his or her trust.
The best way to do this is with food. Find out what kind of treat your trained mice likes best and use this to entice him to do what you want. A simple trick you probably will want to teach your mouse is to crawl into your hand when you call him. You can accomplish this by filling your hand with your mouse’s favorite treat and setting it in his cage. If this is the first time you’ve done this you may want to bring a magazine or watch TV, because it might be awhile before until your little guy is comfortable enough to crawl into your hand.
Once he learns that you are not a danger, but rather a source of snacks, he will warm up to you quickly. After you are at this stage, start making a distinctive noise every time you give your trained mice a treat (a simply succession of clicks or whistles works great). Soon your mouse will learn to associate this noise with being fed a treat and will readily climb into your hand upon hearing it. This is a long process and will take many attempts and hours before its complete, but it will be worth it in the end.