First, a quick overview:

Disconnect the negative battery terminal. If you have the stock radio make sure you have the anti-theft codes for your radio.

You're going to need to move or remove the air cleaner assembly. Start by loosening the clamps holding the air cleaner assembly in place.

Disconnect the air hose, breather pipe and cable from the air cleaner assembly.

Undo all 6 latches (A) on the air cleaner housing cover and remove the cover.

You should now be able to twist the air cleaner assembly out of the way (or remove it completely).

Disconnect the air control solenoid valve connector from the air cleaner housing.

Undo the three bolts (B) and detach the hose at the clamp points (C).

Now you can remove the bottom tray of air cleaner housing, allowing access to the alternator.

Release tension on the belt by loosening the tensioner and moving it down.

With the belt loose you can loop it off the alternator (or remove it completely)

Disconnect 4P connector and the positive alternator cable from the back of the alternator. To remove the cable first remove the boot on the cable, then remove the 8mm nut underneath attaching the cable to the alternator.

Here's a view the of connectors with the alternator removed:

Remove the alternator mounting bolts - 10mm (A). On my car these required quite a bit of force, so you may want a torque wrench or breaker bar.

Now you can remove the alternator. Alternate between a pulling and pushing motion to slide the alternator out of the mounting bracket (alternator removed in picture).

Installation is the reverse of the removal procedure.