First of all, they know and understand your a student (well a lot of them will). Most of the patients have been in and out of the hospital many times and know how it all works.
I would just start up a conversation with a patient just like I would anyone else...."Hey what are you watching?", and "hey do you want to play some chess?"...or whatever. Most of them want to talk, they know why they are in the hospital, most are really great people!
When I did my rotation we watched tv with the patients, played games, listened to music and talked about concerts we had been to, colored, hung out, went to group therapy with them, talked about their meds and how they were feeling, etc. I had a really good time