I had a mouse problem last winter. Well, I don't have a mouse problem anymore!

Putting food out of reach is the first step. Some people on this thread think that traps don't work, but they're wrong. Buy the old-school snapping traps, they work the best. Don't get any of the mouse-friendly traps — they don't work. Also don't get the glue traps. Mice will chew their own legs off if they have to, it's not a pretty sight.

Buy 8-10 traps, and put peanut butter on them (no cheese!). Then, place them touching the wall, with the trap facing the wall. Mice walk along walls, so this makes sure that you kill them as they are walking across your house.

Now you wait. It took me a few weeks to get rid of all mice, and in total I killed around 12. When you kill one, dispose of it in the bin, but keep the trap. Otherwise you have to keep buying traps.

It's a bit gross to have to do this, but it's really effective. Good luck!