I just did this friday on my 2007 SRT. The steps are similar, but slightly different from the link posted. From memory:
There were 5 or 6 of the push pins, I took a philips screwdriver and pressed the center in. They came out easily after that. To reinstall, simply push the pin the other way (so the head sticks up).
There were about 6 philips screws. One near the handle (hidden) another below the armrest (hidden), one on the door hinge side of the door and three or four at the very bottom of the door trim.
Once all the above are removed, simply lift from the bottom (pull toward you) and the door panel pivots out. Remaining behind is a rubber weatherstrip system that can be pushed out of the way to get to the mirror bolts. I believe the bolts are 8mm.
To remove the mirror, you also need to remove or really loosen the outer window trim piece. There is a torx head on the end of the door that holds it in place. Once removed, simply lift the molding slightly and it will pop up enough to allow mirror replacement. I believe I did this with the window in the down position.
Replace the mirror, connect the wire harness (if heated or power) reinsert the molding, put the door trim on and bolt it back up. From start to finish taking your time, an hour or less.