I need to replace the fan clutch on my 2001 bmw z3 3.0i

There are two little fasteners at the top side end of either side of the shroud. Just take a very small flat-head screwdriver and pry out the middle pin part (they are just pressed in anyway) and take the outer part. Don't lose them as they should be reusable (unlessed you monkeyed them out with channel-locks, haha). Then slide the shroud up to unhook it from the top AND bottom (note where it hooks at the bottom when you go to put it back in). The fan needs to be unbolted now so the whole thing can be slid out as one piece.

Put some nice pulleys on while you are in there!