Well, it depends on the hospital, and sometimes on how old you are (for instance, they're not going to let a teen drive a cart). When I started volunteering, I was a courier. Basically, I was tasked with pushing the wheelchairs of patients who were being discharged from the hosital. I would go up to there rooms, make small talk, and whisk them away to the parking center. Being a courier was one of the main things a teen could do at that hospital. Also, other times I would deliver items (i.e., urine sample or medical equipment) across the hospital. Most of the time though, my experience was sitting down with the other volunteers and talking until somebody needed one of us. Each volunteer shift was four hours. I did mine once a week.
Another position I held was that of the mail courier. I basically delivered the hospital's mail to all of its departments. It was a good way to get a glimpse of everything, and also provided some interesting experiences.
Hope this gives you an idea of what's possible.