I had the snip 3 weeks ago, let me tell you how it went down for me:
Initial consultancy where the surgeon explains the procedure, and then asks a number of questions regarding your home life etc.
He also explained the success rate statistics and that the operation is non reversible on the NHS, he then asked me to drop my pants so he could explain the procedure. he kind of nips the sperm tubes through your bag and says that is what will be cut, stitched etc.
an appointment was made for approximately 8 weeks later, however I received a phone call the following week saying that there was a cancellation and would I like to attend the vasectomy clinic that afternoon.
Upon arrival I was called into the consultancy room, and was given some paper underwear, and medical gown and a dressing gown and told to change into those items.
Then the nurse went through some more questions and said the surgeon would be with me shortly. He came in and went through more questions and then leg me down to the operating theatre.
I was cleaned with alcohol, then injected into the bag with a tiny needle (more uncomfortable than anything) when I couldn't feel anything he made the first incision, I felt a strange tugging sensation in the bottom of my belly and then he was stitching back up, repeat on the other ball and bobs your uncle.
The entire procedure took less than 15 minutes, I was at the clinic for less then 1 hour and could quite easily go back to work afterwards, although id booked the afternoon off.
I had sex 5 days later, and although the balls were bruised it wasn't too uncomfortable.
What you actually ejaculate pretty much looks the same, and also the same quantity, sex doesn't feel any different and I don't feel like less of a man or anything like that.
TL;DR:
Had snip, was a pretty painless affair, could go back to work the next day and also have sex 1 week later.
Any questions, just ask!