Please do this at your own risk. I am not responsible if you break anything. End legal mumbo jumbo.
Okay, to begin, this was performed on a 1993 318is, two doors, E36, M42, automatic tranny, black on black, build date 01/1993. Your car may differ from mine. If it does, figure it out.
Alright the only parts you are going to need for this DIY is the fuel filter, part number 13-32-1-720-102 for the 318 and #13-32-1-270-038 for the 325 both before 1995. For 1995+ models, 13-32-1-740-985 is your filter. You will also need two more hose clamps.
As for the location of the filter, on early cars, it is located near and/or around the front driver's suspension components. For later cars, it is on the driver's side under the seat region.
Mine was right here:
From that, jack up the car safely and go about taking it off. Now, for those of you who don't know, the fuel filter is actually full of fuel.

So clamp the hoses coming to and from the filter before you take it off so you don't get gas in your eye or something.
To take it off, you'll have to loosen the protective shroud and then go at the hose clamps. Mine were stripped and spikey, hopefully yours are not so you won't have to spend a half hour with a needle nose pliers trying to get the stupid things off. Anyway, start with the red arrow and go to the blue arrows.
Take the filter out, but don't spill the fuel in there everywhere. You'll want to look for rust, corrosion, dirt or what have you in the fuel to diagnose other potential problems. Mine cam out clear!
Alright, here comes the hardest part: putting the arrows so they point towards the front of the car. Yeah, I know.
Slide the new filter into the protective shield and put on new hose clamps. Secure the shield back where you found it.

Your done. That's it.
When you start your car for the first time, it will start fairly slow. Don't worry, that's because you took some out with the filter. Fuel filters should be changed every 6000 miles, and when it's so easy, why not?