I did this at the same time I installed my O/H console. If you are doing just a mirror, it is a very, very easy project. There are three wires that come off the mirror - power, ground, and one wire to the reverse circuit.
You have an 01 so I can't help you with wire colors and location, but if you have a manual this will be very easy to figure out.
I picked up my mirror at a salvage yard for $5. Either the guy didn't notice it was a auto dimmer or he didn't care, because I gotta believe they would normally charge more for it.
A few hints - if you find a mirror at a salvage yard don't forget to get the connector. If you use a small gauge wire (OEM for the mirror was 22 AWG) you won't need to remove your headliner or A-Pillar cover. Just tuck the wires up in there.
I hope this helps,
Ryan