Apart from whatever method you use to catch them - and I usually use snap traps, though there is a thing called the Mechanical Cat, I think, which is a complicated live trap - you should also study their habits and act accordingly.

Mice scent their trails with urine, so you should clear out all your closets, and clear the tops of the closets, and wash them and then rinse with highly scented water - I use citronella, which mice (and insects) don't like.

(I wouldn't use mothballs, though, because modern mothballs have naptha in them, which isn't good for *you*, either.)

The other thing you have to do is wash all the clothes - and the drawers and closets where they're stored. Throw out all food that isn't stored in airtight containers, and wash the outsides of all airtight containers, and again, rinse them with scented water. Wear rubber gloves.

Wash all the floors, and all the carpets, in the same way.

This works (in conjunction with traps) for two reasons: it disorients the mice, by erasing their trails, and it cleans away the urine which can transmit diseases.

If you keep trapping, and keep wiping out their scent, the mice will leave and not come back.