This is really a very big question you are asking, so even if I could give you a detailed answer I doubt I'd have the time.... but I do have a suggestion, take a look at Greg Linden's blog and his papers on item-based collaborative filtering. Greg implemented the idea of recommendations engines at Amazon using the item based approach, he really knows his stuff and his blog and papers are very readable.
Blog: http://glinden.blogspot.com/
Paper: http://www.computer.org/portal/web/csdl/doi/10.1109/MIC.2003.1167344 (I'm afraid you need to log in to read it in full, as you are a CS student this should be possible).
Edit
You could also take a look at Infer.Net, they include an example of building a recommender system for movie data.
