One of my daughters had her tonsils out at 4 years old because it was affecting her sleep and breathing.
Ours was a day surgery - we went down to Children's in the morning and we were back home by late afternoon. We initially started out in a typical office type waiting room for checking. They gave her the wristbands here, took her vitals and weight. Then after going back to the waiting room for some time, we were called to back and put in a hospital type room. Here we changed into a gown and they gave her "happy juice" which made her quite silly and very relaxed so that they could easily put in the IV for sedation.
A short time later she was taken away for the surgery. When surgery was complete they took us to the recovery room, which had many post op patients lined up "recovering". She had already woken up by the time we got back there and she was crying a little, but I think it was mostly the disorientation of being in that room. The nurse quickly brought her a gift, some pretend jewelry, that made everything okay.
Then we were returned to the hospital room where she was given a popsicle. We were given our instructions and once they were sure she was keeping the popsicle down, we were able to dress and she was wheeled out for discharge.
Recovery went pretty easy, lots of pudding, ice cream and jello for about a week. The one thing we weren't prepared for was her bad breath. She could clear an entire room with how bad her breath was after the surgery. But other than than, everything was pretty easy for us.
Good to take care of all of this before they start school. Good luck!