I had my first full anesthesia experience as an adult - emergency but minor surgery, so not an extremely scary ordeal. I was very distinctly trying to pay attention to the process of going under, as in: do i feel it fade? etc.
I remember doing the countdown thing and also trying to see if i could notice it at all like going to sleep. but, just like an off switch, no state change, just a full stop (but without something like "blackness"). First woke up to voices of nurses chitchatting across the recovery room and knowing everything was okay.
But as another comment put it, I can only imagine death being similar (if instant/unexpected/while sleeping/etc), just without the coming back. Which is scarier.