STOP! Read entire DIY before proceeding.

Note that this is only for the 328i and 328xi, which have the GM 6L45R transmission. If you have the ZF transmission, use Chriztofor's excellent DIY, here: http://www.e90post.com/forums/showthread.php?t=367729

Before I begin, please note that I noticed a barely audible slow tap in my transmission (once every second to 1 1/2 seconds) after doing this DIY. I don't know if I screwed something up; I will have to check with my indy mechanic and report back. I suspect that I dislodged some sediment and partially blocked a component. Since returning home and allowing the car to cool, the slow tap is gone.
I got no warnings of any malfunctions.

Materials: Attachment 1
My first step was ordering several parts from Tisher:
Transmission filter (# 24-11-7-593-565) $45.70
Gasket (# 24-11-7-572-618) $41.92
Parts I ordered from Tisher but didn't need or use:
Magnet (24-11-7-572-619) $1.66
Oil Drain plus (24-11-7-572-622) $3.83
Set of pan bolts (24-11-7-581-606) $11.05
I didn't mind ordering extra parts because I'd rather pay a few extra bucks and not need these items than need the parts and have to special order them halfway through the project. As you can see, they were very cheap parts.

Other stuff:
Transfer Pump $9.99 at Harbor Freight
11 quarts Dexron 6 at Walmart $4.19/quart. I only needed 6 quarts; 7 or 8 would keep you safe.
One tube of gasket seal - not used. Not needed.

Steps:
Once the car is raised,
1) Remove undercarriage shield under the transmission.
2) - optional. Remove filler plug (image 7). Careful, you will have about a quart of transmission fluid come out at that time because you do not have your car running.
3) Remove drain plug (image 7).
4) Once transmission fluid is drained, remove transmission pan. There will still be some transmission fluid remaining in the pan when you remove it. It has 17 bolts, 10 mm.
5) Wipe dirt off of the transmission pan. Also remove, clean, and reinstall the magnet on the bottom of the pan. Image 9, 10
6) Remove the transmission filter. Image 11 It takes a bit of force to pull it out from the transmission, as the neck of the filter is near the top of the transmission.
7) Remove and replace the transmission filter O ring. Image 12. I was unable to and left the old one in place rather than put in a new one. When you remove the filter, it has a long neck to bring the filtered fluid into the top of the transmission. The O ring is located near where the top of the filter goes.
8) Install new transmission filter. Make sure to push it firmly into place. I was a bit cautious, as it's all plastic.
9) Put gasket on transmission pan and reinstall the pan. See image 14 for the bolt tightening sequence.
10) Fill transmission with Dexron VI using the transfer pump through the fill hole until fluid starts to come out of the fill hole.
11) Start car and continue filling with Dexron. The reason why you are able to put in more Dexron at this point is that the Dexron at the bottom of the pan is being drawn up through the transmission filter, allowing you to put more Dexron into the transmission pan. Once the transmission fluid starts coming out of the hole, put the filler plug back in.
12) While keeping engine running, put foot on pedal and shift through all gears several times at idle.
13) Check fluid level. ... I had some come out when I removed the filler plug. Tighten filler plug when done.
14) Put back undercarriage shield.

I noticed after step 12, I had a slow (once every second to 1 1/2 seconds) barely audible metal on metal tapping sound from the front of the transmission. It was barely noticable; I had to be down on my hands and knees and specifically listen for it while the car is in idle. It was NOT there prior to step 12. I drove home ~23 miles on both highway and secondary roads, stopping several times and getting down, sticking my ear under the car during the drive home and could hear the tapping. Since the car has cooled down, I started the car again and the tapping is gone. There were no warning lights indicating any malfunctions and I did several checks on the way home - all said OK.
I suspect that I dislodged a small piece of sediment and it partially blocked a transmission component for a while. After cooling and restarting, the particle probably dislodged and is now safely nestled in the transmission filter.

I took a sample of my transmission fluid and will send it to Blackstone Labs for analysis. I will report on the results. I had approximately 52,500 miles on my car at the time of change. I may do a partial drain and refill in another year or two but I don't think it's worth changing the filter more than once in a car's lifetime. The filter's pretty robust.

I'd like to say thanks to Chriztofor and Entity for their help through PMs.

Image details:
I went to the Davis Monthan AFB auto hobby shop to do the work (image 2)
Once on the lift, I took a picture from underneath the car looking at the front (image 3)
Once you remove the undercarriage shield below the transmission, you'll see this sticker on the bottom of the transmission (image 4) ... the BMW part number 83220397114 is also known as Dexron VI. From my readings on Dexron VI, it is only manufactured by a very few companies and the specs are pretty tight so you can buy the cheapest you can find and still feel comfortable. I chose to buy the Walmart branded Dexron VI ... it took me four different Walmarts over the course of a couple of weeks to accumulate 11 quarts.
There is a plate specifying GM 6L45R transmission on the driver's side of the transmission (image 5) - sorry the picture didn't turn out well.
Image 6 shows the transmission from behind (toward trunk) with the drain plug (I think it was 5 hex key) on the bottom of the pan and the fill bolt (17 mm) above it on the back of the transmission .
Image 7 shows the fluid draining.
Image 8 shows the transmission with the pan removed.
Image 9 shows the pan with the magnet. I have reinstalled the drain plug, above the magnet.
Image 10 shows the magnet after cleaning it. Note how dirty the paper towel is after cleaning the magnet.
Image 11 shows the old transmission filter.
Image 12 shows the transmission filter O ring in place in the transmission.
Image 13 shows the pan gasket and pan. Note the raised bump on the corner; it fits in the smaller hole on the pan. There are two of these on the pan and gasket. It's impossible to put the gasket in improperly.
Image 14. Transmission pan bolt tightening sequence.