We had this with DS, it was found at his 3 day check. Urology investigated, they looked at his scrotum, and the bulge in his groin area (which we thought was a hernia), and said 'yep that needs fixing'. They referred him for surgery, which he had at about 11 months old. It was done as a day surgery at Alder Hey Hospital, under general anasthetic. He had to have no food or milk from midnight the day of the surgery, and we had to be at the hospital for about 6am if I remember rightly. The being at hospital part I remember vividly. They gave him a tiny hospital gown, put numbing cream on his hands so they could put a canula in. They put him under the anasthetic, and then took him off to do the surgery.
The surgery is called an Orchidopexy. They drew the teste down and secured it, he had a few tiny stitches in his scrotum, and some in his groin, the incisions they made were really small. He was grumpy and groggy after the anasthetic, and he was absolutely fine a few days later. His hands were a bit sore for a few days as well from the canulas. He's six now though, and you would never know he had to have it done.
I think it was harder for me and my DH than for DS! He was our first baby and our only one at that point, and I held him while they put him under anasthetic, which I found really scary. Then the wait while they did the surgery, and then woke him up felt like the longest time of my life. But the staff at Alder Hey were absolutely wonderful with him and with us. While they were putting him under one of the nurses blew bubbles to keep him entertained and stop him feeling scared.
DS had a check up a little while later, I think it was about 6 months after the surgery, and they were really happy with him, everything was fine, and he's had no further issues since.