I have questions(tube removal)

I spoke with my dr yesterday about getting things permanently taken care of after this baby and even though I asked lots of questions I still have more and wondered if anyone could answer them for me. My hospital doesn't tie off tubes or burn the ends they completely remover both tubes. I feel that after talking to my dr this is a great option for me and my family. However I have NEVER had a surgery. I have never been put under and I am so scared even though its four months away. Do they put you under in the operating room where you see everything? Or do they do it in the room so you are more relaxed? She said I would have small incisions and a few stitches and just be sore for a few weeks. Has anyone had problems? Is it hard to care for a baby this way? She also made it sound like they would do it not long after I had baby so It sounded like they would do it the same week maybe the same day? Any advice or answers would really ease my mind. I would google it but I don't want to completely scare myself... thanks in advance for any advice!