Are you going in overnight or day surgery? You get taken to the anaesthetists room, and you are on the bed while they chat to you, make you feel at ease. They've literally seen all sorts of people- most people are very nervous so completely normal and they are used to it.
I actually can't remember the actual how it was given part but essentially, you are talking to them one second and the next you wake up in the recovery room. Absolutely no recollection.
There's usually lots of nurses fussing over you as you wake up, lots of beepy machines. You don't really feel anything initially, no pain, just you aren't quite awake yet. It's not uncommon for people to say funny things - I think I was chatting nonsense for a few minutes. Totally normal.
After major surgery you are usually given a clicker in your hand to allow you to self administer morphine, its set to a limit so you cannot have too much, that keeps any pain under control and you are still fairly sedated for the first few hours. At some point the surgeons come back and see how you are and let you know how it went.
I've had two one for knee, and one for a major organ. Main thing is more the recovery back home, staying on top of any soreness with pain relief, lots of sleep etc. You will be fine.