Having done this before on my E46, I felt competent to tackle the work given the help from this thread on removing the airbag & wheel.
However, my E46 wheel came with all the switchgear installed and it was not clear how difficult it would be to swap these over.
First, follow instructions on airbag removal in link above & make sure to disconnect the battery before messing with the airbag.
The airbag is more difficult to remove than on my E46 and the E90. There is a soft wrapper around the unit, similar to a very wide rubber band that makes it more difficult to extract from the wheel once you have popped the retaining spring. Once you had the first spring released in the E46, you knew it, as the bag was very loose. Not so with the F30.
Slowly remove the airbag and pop the black connector and then note how the white connector is stuffed into a small recess at the top. You will need to make sure you stuff it back in there on re-assembly.
Once the wheel is off, you need to remove the switchgear. There are 2 screws accessed from the back of the wheel (Torx 20) that first have to be removed.
After the screws are backed out, you need to pry the whole trim+switch assembly from the wheel. Start on one side near the switch and slowly start pulling out. You should soon feel some give as the tab is pulled out of the retaining hole in the wheel. I pulled out the 2 on each side and the did the one at the bottom last. I highlighted these tabs in the picture below.
From here, it's easy to reverse the process and press the switchgear/trim into the new wheel, reconnect the cables and re-attached the wheel and pop the airbag assembly back in.
After connecting the cables to the airbag, be sure to stuff the white connector back into the recess at the top inside of the wheel.