See LED Throwie Rodents, Conjoined Twin Mice, and Duck Mouse for more advanced projects..
Step 1: Procure mice
These came frozen from the East Bay Vivarium. Most pet stores will happily sell you pet or feeder mice, but they may not exhibit such nice color variation. They may also be alive; if so, you'll need to be able to fix that yourself or find another supplier. Choose wisely.
Mice can be stored in ziplock baggies in your freezer until you need them. Don't repeatedly freeze/thaw your mouse or leave it in the fridge for an extended period as this decreases the skin/hair quality. An hour or so at room temperature is usually sufficient to thaw your mouse.
Step 2: Assemble tools
plastic to cover your work surface (a trash bag does nicely)
beads (for eyeball replacement)
fine scissors (nail scissors are OK)
scalpel (X-Acto knife is OK)
fine-gauge wire (I've got 26 gauge)
thicker wire (mine's not marked, but is probably 12-15 gauge.)
thread (close to fur color is preferable)
Step 3: Cut wires
4 x 9" thin (26 gauge) wire
1 x 12" thin (26 gauge) wire
1 x 16" thicker (~15 gauge) wire
Note that the lengths may vary a bit due to the size of your mouse.