Not annoying at all. I've had surgery 3 times and each time it was different, but in each case you just fall asleep and you're out like a light until they wake you up.
The first time they wheeled me into the operating room before administering the anesthetic. I remember it being freezing cold in there and they had to put heated blankets over me because I was shivering. Drugs were administered via an IV. In this instance, I woke up in the recovery room with a nurse at bedside.
My second surgery, they used gas to anesthetize me. I was in the surgical prep room when they put a mask over my face and told me to take deep breaths. I remember really trying to suck in as much gas as I could to make sure I'd be out.
That may have worked against me though, because I got pneumonia and wound up being in the hospital for 9 days. In that instance, I don't remember being in recovery, just waking up in my room with family around me.
This last time it was easy breezy. They used an IV to deliver the drugs and they did it in the prep room (never saw the surgical area). I woke up back where it all started with the anesthetist telling me to open my eyes. I kept falling back asleep and because of my severe sleep apnea, my oxygen levels kept dropping. He stayed by my side until my oxygen levels stabilized. Next thing I know, I'm in my room hitting the morphine button. (Love that button!)