Found this guide on E46Fanatics DIY section, you can see the full post here: http://www.e46fanatics.com/howto/howtodetail.php?howto_id=7 but know that it contains much more than simply the sidemarker install (which is why we pulled it apart)
14. There are two ways this can be done, with a credit card, and by hand. I recommend doing this by hand to minimize the risk of scratching the car. Using both hands grab onto the side indicator. If you are using a credit card slide it under the rear of the indicator.
15. Push indicator forward to compress the retainer clip.
16. Grab the rear edge of the indicator and pull it out.
17. To fully remove the indicator from the fender turn it 90 degrees so it is pointing up and pull it out.
18. Disconnect the bulb socket by turning it. Leave the socket connected to the wire. If you are replacing the bulbs now is the time to do it.
19. Insert the bulb into the clear indicator and lock socket in by turning it.
20. Insert front of indicator with metal clip in the fender hole, push forward and snap the rear of the indicator in, it will snap in.
Or check this one out, directly from BMW themselves:
|Removing and installing/replacing front left or right additional turn signal lamp (saloon/sedan, touring)|
|Special tools required:
64 1 020
|Up to 09/2001:
Lever out additional front turn signal lamp ① with special tool\~ 64 1 020
Pull out additional front turn signal lamp ① up to bulb holder, turn through approx.\~90° and feed out.
Unclip additional front turn signal lamp ① in direction of arrow and remove.
Disconnect plug connection ① and remove additional front turn signal lamp ②.