Mouse traps that are properly baited and properly set to catch the mouse are very effective.
When using mouse traps you need to put some cheese or a piece of meat, peanut butter etc onto the mouse trap and make sure it's not easy for the food to come off of the mouse trap.
The mouse needs to work at getting the food off the mouse trap so that the mouse trap releases and then traps the mouse.
A snap mouse trap should near immediately snap down on the mouses neck and kill then within a minute or two.
Be sure to check mouse traps often so that other mice do not see the dead mouse and avoid the mouse traps.
The mice can see the dead mouse and realize that the mouse trap is dangerous and something to avoid.
Glue mouse traps are also a good effective way at catching mice as well.
You should also put a little bit of bait such as cheese, meat etc onto the glue mouse trap so that they are attracted to it.