In all of the years that I have worked on this machine, I have found no good way to remove the fan.

The best way to start, is to push in here on the side of the fan.

Being careful not to exert too much force, try to push in, and wiggle the fan outward as such. (2nd Photo)

You can now lift the fan all the way out, and remove it.

The Fan Power Contacts on the Logic Board: