I work part time in a library in Nottingham (have had the job nearly three years now!)
Obviously every where will be different but mine had a couple of sections. First was a 'trolley test' or something (can't remember exaclty what they called it). The had a trolley with some fiction books on and another with non-fiction books. I had to put both sets in order, so fiction are just in alphabetical order of surname, (just look out for double barrelled names, and names like 'Daphne Du Maurier' etc, which can trip people up.) There are usually a few with the same first letter so you have to look at the second one etc. Non-fic are normally in the dewey order (the numbers on the spine), which is pretty easy. I also had to fill out a cash form, which had various numbers in for denominations of money, I just add to add them up, again pretty easy really!
Then there was the interview (mine had three people, the senior library assistant for the library I would be at, the area librarian and someone from the council.) Questions were similar to Moniker, like her I was a library prefect at school, so they asked a bit about that. They wanted examples of what I could bring to the library, why I wanted the job, what type of person I felt I was (strengths and weaknesses etc). Also, talked about what I thought the role of libraries is/should be. Stuff about equal opps, they wanted examples of what the library had done/could done - things like a lift, hearing loop thing (can't remember the name of them!), large print books, spoken word, language line translation service, shelves low enough for everyone to be able to reach etc.
I didn't have a role play, but they did fish around for info on what books I had read etc. I have done my duke of edinburgh award and they asked me about what I had gained from that, and what I had done for it, they used that to lead onto what I like doing and as soon as I mentioned reading they jumped on it and asked what I liked reading. Mentioned a few books, which they talked fairly 'casually' about. I would guess though that a lot of people would talk about books at a library interview because they think they should, and it felt like they were checking that I wasn't making them up. Obviously, of anything like that comes up just talk about books you have read, not things you think will look good.
Thats all I can think of! As moniker said, ask if you have any more questions!