"Build a better mouse trap..."
Well you don't need to build a new mouse trap. The old standard works great with a slight modification and the proper use use bait.
Once you have your trap modified and baited properly, there are three things that are very important to catching mice: location, location, location.
Step 1: The trap
There are many different types of traps you can purchase to catch mice. Some are kill traps and some are live traps. If you chose to use a live trap, ask yourself why? If it is to be nice to the mouse or you can't deal with a dead mouse keep this in mind.
If you release the mice back into your yard, they will come back in! They don't want to be out in the cold when they know your house is nice and warm and stocked with yummy food. There are also live traps that may keep the mouse alive but to what end!
There is that sticky paper type where the mouse sticks to the trap. I have not used them but I have seen the results of their use. The mouse will not like being stuck to this and they will get themselves free. I have seen what they leave behind, stuck to the paper. I won't go into that here.
As un-PC as this may sound, just kill the mice. Get a good old spring trap, bait it, set it, kill the mice. Normally, where it one, there are several.
There are some fancy kill traps that are easy to set, easy to clean, etc... But they do not work as well as the good old fashioned spring trap. If you want catching mice to be easy, hire an exterminator to come in and take care of the problem. If you want to catch mice, you will have to do a little work and get your hand dirty.
If you don't like getting your hands dirty, wear gloves!