I was on one of those probably 10 years or so ago. As Blondie described, we would work with the local hospital (in my case it was a Catholic hospital) and I actually got a clergy parking pass (LOL - I think I still have it, never used it but I thought it was funny). On the week I was assigned, I'd call the chaplain to ask if any JWs were in the hospital and needed a visit every other day. I'd pop down there, check to see if their elders had been visiting them. Sometimes they would say no and being the uber zealous elder I was I would find out what congregation they were in and call the PO. It wasn't a big deal, I'd do the daily text or something with them and then offer a prayer. 10 minute visit tops unless they really needed something which in most cases they had family or folks from the hall already helping them.
Honestly, most weeks there would be no one on the list. That's why I started calling the chaplain (great guy by the way) instead of wasting time going to the hospital.
We only visited those who specifically requested a visit from a JW minister. Since it was a Catholic hospital, I think in that case the chaplain did most of the visiting but had a list of other religions with ministers available to met their patients needs.
Overall I thought it was a nice program.