Mice that invade your home can chew electrical wires and insulation. What's worse, they can dirty up parts of your home with dirt and droppings. Mice breed quickly, so a family of half a dozen mice can multiply in a short time. Catching mice in a humane trap and letting them go is one option, but consider that if you don't let them go at least three miles away from your home, they can find their way back. Also, if they don't come back to your home, chances are they'll move into another one.
Purchase mousetraps, placing them in areas where you have found droppings: in cupboards, under sinks or at the back of toilets are common places, as are build-up areas and basements (also close to baseboards). Don't bother trying to place the traps in the ceiling, as the mice will make their way to the food on the traps. Cheese is generally known to attract mice, but peanut butter is better as it is both attractive to mice and it can't be pulled off the trap in one piece and then eaten. Consequently, there's a greater chance that the mouse will be caught.
Set out trays of poison in the same areas in place of the mousetraps, if you don't want to deal with traps. The positive for this method is that poison is much more effective. The trays themselves (usually about 3 inches square) are designed so you don't have to touch the poison (though always wear gloves when handling poison trays). Mice tend to get the poison on their fur, and carry it to other locations mice inhabit. You will know you have been successful as the trays will become empty in a few days (or sometimes, in a few hours). The negatives to this method are that if you have small children of animals, the trays have to be placed in areas where they absolutely cannot be interacted with. Also, as the mice will die, you will find some dead mice in you home but probably not all.
Discard all dead mice in a thick plastic garden refuse bag (especially if they have been poisoned). Discard your gloves, also. If using traps, set the traps a second and third time, and more until there are no more scratching noises coming from your ceiling.
When placing peanut butter on the trap, be careful when you set the trap as it can easily snap on your fingers. Always wear gloves when discarding dead mice. Always read the instructions on the mouse poison packets and follow every step.