The key to efficiency is good help. I am incredibly spoiled. Obviously this is rarely the case in residency.
Our anesthesia techs get the room set to our preferences, so I can walk in and be ready to start the case in about 3 minutes of prep in the morning, same during the day between cases, although I spend most of those minutes during the prior case. When I get to the room all I have to do is a final check of the machine.
The patients have monitors placed in preop so all that is needed is to hook them up to the OR.
The patient enters the room, and from that point until patient is intubated I have the undivided attention of the circulating nurse and frequently another person. Because I work at a friendly hospital this second person is often the surgeon. I never would have dreamed of having the surgeon put on a moniter, start a second IV, set up the warmer during residency, but it is awesome.
The circulating nurse can hook the monitors up as I talk to the patient, and grab my preinduction drugs, and place the mask in the tube holder so it gently sits on their face. BP cuff first. "Deep, easy breaths" as BP cuff runs.
Time to fall asleep.
If I do an art line the techs have set up a tray exactly like I like it. If I do a central line they set up the tray ahead of time, and scrub in with me, handing me what I want when I want it.
The only downside of this set up is that your wife will start to wonder why you are so lazy and ask her to get you things that are on the counter right next to you.
Edit: I forgot to mention one thing I feel really adds to efficiency. Once you start a task, take the appropriate amount of time to do it right. Rush set up if needed, but never rush once the needle hits the skin. Time saved on performing a single attempt slowly is much greater than 2 or 3 attempts fast, and you look much better to patients and other staff.