I just did my '98 driver's mirror, but I imagine that the '01 version isn't vastly different...
Assuming you have electric mirrors:
1) Carefully prise out the round mirror control panel from its housing and disconnect the wiring.
2) Pull off the housing itself (note that the clip nearest the front of the car pulls out towards the seat and the two at the back pull off towards the rear of the car).
3) Disconnect the mirror cable and carefully prise the fixed connector off the door.
3) Unscrew the six screws around the outside of the door card (two at the front, two along the bottom and two at the back).
4) Carefully prise out the circular cover behind the door opener and remove the screw beneath.
5) Carefully prise out the insert in the door handle (this can be difficult) and remove the two screws beneath.
6) Pull the door card away from the door and carefully pull off the foam around the mirror area.
7) Hidden under the foam and sealing tape is a hole that allows you to undo the single 10mm bolt that holds the mirror on - but before removing the mirror prise out the cable grommet and pull the mirror cable out (the grommet is split to allow this). Be very careful not to drop the bolt into the space between the door skins as you remove it and be sure to support the mirror too!!
8) Once you have bolted the new mirror on, be sure to re-fit the foam and position cables etc as you found them.
9) As they say - refitting is the reverse of removal!!
Good luck!
daKlone
March 2007