Hi R.,
I have not had a tubal ligation, but I have been put under a few times. It is nothing to worry about.
An anesthesiologist is a specially trainied doctor who knows exactly how much drug to adminsiter to make sure you wake up in a reasonable amount of time. You have nothing to worry about there. This is an extremely precise science with many many safeguards in place.
When you wake up you'll be foggy for a while. You'll probably go in and out of sleep for a little bit and you'll be a little slow for a few hours. Obviously you won't be driving and you should not have any parenting responsibilities.
Sometimes (ask the doctor to see if this is the case with you) a tube is inserted from the mouth down your windpipe to facilitate breathing while you are asleep. This is normal and fine and you would never know about it if no one mentions it. You might wake up with a dry mouth and a scratchy throat (like when you have a cold, nothing major) and you'll be offered water when you wake to make you feel better. You might throw up or you might not. I have once and on 2 other occasions had no nausea. In retrospect, though, it really was not that bad. They are prepared with a pan if you need it. They've seen it all before!
It won't be one of your most energetic days but please do not feel nervous or scared. You will wake up suprisingly pain free and you will be fine!
I wish you peace through it all.
Umber