Note: I first wrote this tutorial when I was a member of bmw-forums, before this site was ever created. I'll change the captions on the images over one day if I get bored, but for now, just ignore them. It's still a good DIY. 
haha
All right, so for those of you who don't know, I recently got my ass kicked by a mailbox, screwing up my passenger side mirror. I said "oops", then realized this would be a great opportunity to upgrade to m3 mirrors. (I'd hate to see what happens if I ever total my car, haha)
Here is a DIY on changing them out. It takes between 30 minutes and an hour, depending on how mechanically inclined you are.
My car is a 1997 328i, though I'm pretty sure this procedure is the same on all e36's.
Tools needed: Flat head screwdriver, phillips head screwdriver, heavy duty sandpaper or a dremel (maybe), scissors, 10mm socket wrench, some means of connecting wires (saudering iron, butt connectors, etc), and skills for using your fingers (which I'm sure most of us have plenty of, haha)
This DIY will be very heavy on photos, as I believe in a "picture is worth a thousand words", I hate DIYs without them, as it seems far easier.
Here are what my (and probably yours) stock mirrors looked like:
and this is what they'll look like by the end:
Now, let's begin.
1) First start by popping off the inside panel of your car. Use a flat head screwdriver to get in there, but be careful not to break off the tabs. It might take a bit of force, but they do just pop off. If you do break it, they're $8.80 from the dealership (not that I'd know or anything, lol)
When the panel comes off, you'll notice a bunch of foam and sound proofing material inside. It's probably pretty flakey and won't help much. I discarded mine, but some of you might want to be careful and save it to put back in.
2) Inside you'll find three 10mm bolts holding the mirror on. This is conveniently the same size bolt as the socket in your bmw toolkit in your trunk. In this example I used my own kit though.
Unscrew the bolts, but be careful to hold the mirror on, because when they come loose it will just fall off, pulling hard on the power cord.
At this point it just kinda falls off...
Notice the piece of waterproofing rubber stuck to the mirror. Take that off and don't lose it, you'll use that same piece on your new mirrors.