Differential Fluid Change
I didn't get pics of what I did for the differential fluid change, but I can describe what you need to do.  Most of the recent models of BMW has the "Lifetime Differential Fluid".  I believe that means the fluid is good until the differential goes bad.  I change my differential around 50k miles. 
I use Red Line 75W90 Gear Oil.  It contains the friction modifier for limited slip differentials.  I used this for both my 323IS and M Coupe with no problems.

You will need a pump to fill your diff.  I use the Sta-Lube pump.  You will see why it is necessary to use a pump.
Of course you also need the right tools to do the job.  You'll need a hex wrench.  For my cars I used a 14mm hex socket.  In the end you will need a torque wrench to properly torque it down (it is recommended not to use a torque wrench when loosening bolts).
Now let's find your differential.  From the rear of your car, look underneath.  In the M Coupe it is easily visible.  In the E36 3series, half the diff is blocked by the spare tire well.  The 3 series looks the same except for the cooling fins are not there.  In the picture, you can see 2 arrows.  The top arrow is the fill plug, and the bottom arrow points out the drain plug.

I don't have pics of me draining and filling the the diff, but it is very straightforward.  First loosen the fill plug.  If you can't loosen the fill plug, then don't loosen the drain plug. 
Drain the diff like you would an engine oil change.  Bolt the drain plug back on (50 lb-ft).  Next, fill it back up with your diff fluid using the Sta-lube pump until the fluid reaches the bottom of the fill hole.  Bolt on the fill plug (50 lb-ft).  That's it.  Now drive and enjoy your BMW.
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