I back up, like Daddle, in flat water
and high winds, provided the boat is up to it (and most modern boats I've sailed on have been);
In strong winds and a chop or a swell, I do it like Richard5 in post #2, except from the boarding platform rather than the cockpit
, with a maxi-snapshackle on the end of the line, which runs outside everything to the bow roller, and then back to either the windlass
or right back to a primary winch
In the latter situation I would do it under sail, by heaving to well upwind of the mooring, and adjusting the angle of drift to bring the transom shaving close past the mooring buoy.
In really bad circumstances I have a dinghy
which I store with close-fitting rubber caps on the sharp points, so it doubles as a throwing grapple.
That's how NZ's Fiordland fishermen capture their mooring when it's blowing hard, in the tough boltholes in that area, and further south.
I'd use that either from the cockpit or the swim platform, unless fully crewed and under power:
In that case I'd stand on the windward bow, back a bit from the forestay* to be able to get an unimpeded swing if the helm
mucked up the approach. They should aim to leeward of the buoy, partly so they can still see it, and so I can stand in one place regardless of how well or badly they judge it. (It may not be their fault: there may be a williwaw from an unexpected quarter, too late to correct for)
*(not too close to the inner forestay)
I have limited enthusiasm for catching buoys on my prop ...
and unlimited enthusiasm for putting a bit more thought and effort into refining methods which do not rely on technology, eg engines, against the day when technology takes a little holiday.