The Bentley Manual gives you step by step instructions but it's really pretty easy to do.
On my 91 535 (M30 engine) this is what I had to do - yours might be pretty simaler.
Disconnect the negative post on your battery.
Removal of the cooling fan shroud and fan is helpful but I did mine without removing it.
Disconnect the cooling duct to the alternator.
Disconnect the electrical leads.
Remove the two bolts that hold the alternator - one is a lower thru bolt that is the pivot point for tensioning the belt and the other is the upper bolt that locks it in to place. Loosen the upper one first so you can relieve the belt tension.
Even with the bolts removed, I really had to pull hard on it to get the alternator off of the mounting bracket - it has a pretty tight fit.
I bought a set of ratcheting boxed end wrenches because it was pretty tight trying to get a socket wrench in there. The ratcheting boxed end wrenches saved me a lot of time.
You might also want to slip a piece of cardboard or sheetmetal in front of the radiator to reduce the risk of damaging it.
I did this last month on my 525i I think. Looking at the pictures I took in the past I remembered removing the intake is not necessary. I did remove the fan. But you may do it with the fan in place. It just takes longer.
You need to remove the serpentine belt of course. The top bolt is behind the belt tensioner pulley in the picture. The most difficult part in the removal process is loosening two wires on the alternator. One needs a 10 mm socket. The big red battery cable needs a 13 mm socket. Access to these two nuts is limited. But compared to the 540 it is a piece of cake.