I had knee surgery in 2011, and I felt the same way. I almost would have preferred that they do a local anesthetic and have at it. They used Propofol and it was fine. I didn't feel well rested like others here, but I didn't feel bad either. I was a bit confused when I woke up, too. That lasted mere seconds though as a slight throbbing in my knee reminded me what I was doing there. I was actually thankful for that.
As for the actual experience, they started by putting an IV of saline in my arm. Then the anesthesiologist said, "You'll feel some coolness in your arm," when the actual med starts flowing, which I did. Then I lay there for a bit, but I noticed that there was an attendant down by my feet working on something in a sink. It was bugging me (must have been the drug talking) so I closed my eyes so I wouldn't have to see him. Then I thought to myself, "they probably think I'm asleep, but I'm not," so I opened my eyes again to prove I wasn't. Next thing I knew I was waking up. Not so much that it felt like instant, but more like you might feel when you have a great night's sleep and suddenly it's morning. You're aware that time has elapsed, but just not how much.
The staff was great, and they were very gentle with me during the whole process. They took time to answer my questions while I was getting hooked up, for which I was grateful. Overall, the experience was totally fine.