(You consider using poison, but you realize it would be a mistake. They usually crawl into the walls to die, but not always. Sometimes they die in shoes or coolers or under your sofa (see "childhood trauma" above). And the whole idea is to get rid of them without having to see them. Ever.)
Step 1: Gather Stuff
Paper grocery bag
Spring-loaded mousetrap (the killing kind)
Strip of paper (not pictured)
Step 2: Prep the Mousetrap
Lift the kill bar and feed the strip of paper under it.
Step 3: Prep the Bag
Cut a horizontal slit in the bottom of the bag, near the bottom edge where it is resting on the table. The slit should be slightly wider than the paper flag that is glued to the trap.
Step 4: Mount the Trap in the Bag
(This and many subsequent photos were taken through a cut-away portion of the bag for demonstration purposes. You should leave your bag intact to protect your sensitive eyes from having to gaze upon dead rodents.)
Step 5: Set the Trap
Set the trap in the normal manner, then feed the end of the flag through the slit so that it is looped over the kill bar.
Tear off the flag so that only a few centimeters extend out of the bag. This will ensure that the entire flag is pulled inside when the trap is sprung.
You might want to fold a handy entrance ramp at the opening for your mice guests. You want to make it as easy as possible for them, right?
Step 6: Wait for a Critter to Meet Its Doom!
Step 7: Dispose of the Whole Death Chamber
Repeat as necessary.
Some people will complain that you are wasteful not to simply empty the trap and reuse it. Those people are insane. Traps are dirt cheap, and you can make a new death chamber in five minutes. That's a small price to pay to avoid the jibblies.