Depends on the situation:
Shore diving: Stepping in the water /surf with fins in hand or clipped off on the manometer. When I get about chest level in, put the fins on (springstraps).
Boatdiving: depends on the situation and the team. Current, wave and wind action (fetch), rolling and stamping of the boat, if we drop from an anchored boat or drifting to a dredged buoy, experience of the team, etc. This saturday I'll be taking a guy on his first North Sea wreck dives... so he's going to drop in fully set (mask on, wing inflated, reg in mouth and fins on). With an experienced crew I've dropped in stage/scooter and a fin in a hand, mask clipped off, hood pulled back knowing there was a lot of current. It doesn't matter if you act fast (put on fin, clip of stage) and start slowly finning against current. Having your hood off and mask still of helps with situational awareness in some cases (you hear and see better). This is North Sea and Medditeranean wreck diving.
Good trick if the boat is rolling badly is to put 1 fin on... and keep the other off... you'll have more stability and still have at least 1 fin on when you hit the water, saving time.
So it all depends on the situation... in any case things like valves shut, wing not working, etc are checked as a group before hitting the drink as a group.