I just did it; with a steel 1/4" (I think) bit. There are a few different kinds, I've installed two, both the standard round chrome mirror, not a sport mirror or anything... but the first time I did it, the base of the mirror has these outward facing bumps that have to correspond with inward facing bumps on the sheetmetal of the door. I believe this may be for remote mirrors only- I'm not sure. But that was a challenge, because both the sheetmetal had to be bent inward and then I had to find the backing plate that also had those bumps (it did not come with my mirror). The most recent one had more of a flat bottom with only the studs sticking out. Super easy install. Just had to prime and paint where I drilled through so it wouldn't rust. Gaskets are tricky (again, the ones I've bought did not have them, so I had to make my own).
I generally measure from the leading edge of the door back to the beginning of the mirror base. Since the leading edge was at an angle, make sure to note that and repeat it on the passenger side.
Then I measure down from either the bottom of the window opening, or a character line in the metal. Then from the leading edge of the door handle to the trailing edge of the base, and then for fun the bottom edge of the door to the bottom of the base. I (tried to) replicate the exact measurements from the driver's door to the passenger side- this is the first post I've seen where the passenger side may be in a differing location, but it makes sense.
I hope this helps- if you have any other questions, I will try to help as best I can.