In reply to WillC:
I think the most important aspect of efficiency is that, at the stances, the two climbers should always be working on different tasks, and neither should be idle.
So, for example, an obvious time-waster is having one climber hand gear over to the other piece by piece. The second should clean everything onto an over-the-shoulder sling, which is handed (with care!) to the leader. While the leader is racking, the second should be doing other things, such as restacking the rope, adjusting his or her tie-in, and and setting up the belay for the leader.
The same principle applies when the leader and second are a pitch apart. Whenever possible, the leader should clip into the first anchor piece placed and call off belay (I love the wishful thinking of screaming "safe" into the howling gale), so that the second can start getting ready. I think this works best if the leader has an installed tether for the purpose.
The second should be clipped to one of the anchor pieces, also with a tether, so that as soon as the leader has gone off belay, the second can start getting ready to climb (put on/tighten shoes, put on the pack, take apart all but the last anchor piece and stow the cordelette if one is used). When the leader has finished the anchor and pulled up the rope, the second should be ready to climb as soon as they are on belay, with only the slight delay of unclipping the tether and removing the last anchor piece.
Getting back to the original question, when the second reaches the stance, they immediately clip their tether to one of the anchor pieces so that the leader can get off belay and so that the second is set up for an efficient departure later on. The second hands the leader the sling with all the gear and then proceeds to anchor themselves with the rope and restack the pile while the leader is reracking the gear and perhaps checking the topo.