I had the Nissen in October 2007. They wrap the fundus (top portion) of your stomach around the esophagus and sew it. The best description I have ever seen for this procedure is at this website
I am not posting it as an advertisement for Dr. Fusco, I am posting it because it has a great pictorial view of the procedure that is not bloody. It is extremely informative. If you read the other posts on this board, especially the ones entitled Post Nissen Fundoplication Hiatal Hernia you will find a ton of information.
I'm sure that other regulars posting on this site are sick of hearing me state this, but I chose the name HappilyWrapped for a reason. It was the best decision I ever made.
As to not vomiting, that is not a definite. Some people can, some cannot. Some people can burp, others cannot. It all depends on how tight your surgeon makes the wrap. In the old days, burping and vomiting was definitely not going to happen. The procedure has changed a bit and the wraps aren't done as tight as they used to be. I have been able to burp since the day after surgery with no problem. I have not had a reason to vomit, however, after a recent endoscopy the doctor said he saw no physical reason why I would not be able to. You wouldn't want to vomit soon after surgery because you wouldn't want to damage the wrap, but a few months later it should be healed and vomiting would be OK.
If you had food poisoning and could not vomit, you would go to the ER and have your stomach pumped. If you had the flu you would just feel lousy.
There is no guarantee that the surgery will work - it's not 100% for everybody. Of course, no procedure carries any guarantees because every human being's insides are similar yet different. However, you will find enough information in this area to read about good and not perfect outcomes. Pour a cup of tea, settle back, and do a lot of reading through the old posts. You will be able to have a very good conversation with your doctor after you are done reading.