Also, it is rarely appreciated to hear, "I know EXACTLY how you feel" in any mourning situation, and/or listen to other tales of grief. Grief can be a very selfish emotion, so show your support the way you wished others had- offer to listen, cry with them, etc.
I would add that humor is usually not forbidden, except perhaps in the very early stages (dissent is welcome on this, as it is something I'm trying to figure out). Recalling how Fluffy's tounge would hang out of the side of his mouth when sleeping can be very appreciated.