Annie
The first thing is to know that for most people everything goes very well indeed. Everything will be explained at your son's pre-theatre assessment.
In Glasgow the routine is more-or-less like this: Nothing to eat after midnight on the day before the surgery, and report to the hospital at 0800. Transplants are done first on the list so there is not long to wait. Before leaving the ward, Glasgow patients are given a huge box with the words "Human Tissue for Transplant" emblazoned in large blue friendly letters.
Then there is a bit of a wait in the theatre reception area. They check that you are the right person and make sure that you have signed everything that needs to be signed. The surgeon came out to say hello.
Then to the anesthetic room. They take blood pressure (again), and chat away. A needle is inserted and the patient falls fast asleep.
When I awoke I was in recovery, wearing an eye shield and a nurse was saying that I could go back to the ward.
At the ward they offered lunch, but I preferred to sleep.
The surgeon came to the ward and explained what he had done and that I had 16 sutures holding my new cornea in place. Because I live a distance from the hospital they kept me in overnight. First thing the next day I attended a clinic and all was well. My wife came to collect me and we returned home.
4 weeks later I had another clinic and all was well. The sutures remained in place for 18 months before the first of them was removed and then another six months or so before the rest came out. It then took 4 - 6 weeks for my vision to stabilize so that it was worthwhile having glasses made.
I now have better than 6/6 vision using specs for my right eye and a contact lens for my left.
Tell your son that he will be in all our thoughts. He may not be able to pick up his baby for a little while, but that does not mean that somebody else cannot pick her up and hand her to him! Your daughter in law does not really need to peel grapes for him (although she may like to do so

), but should be aware that for six weeks or so he is advised not to bend over or do any heavy lifting.
All the best
Andrew