As an undergraduate, you can study German film in the 1st-year, as part of the Prelims Course if you are doing German Sole, in the 2nd or 4th year, as part of the Modern German Period Paper (Paper VIII), and in the 4th year as part of the European Cinema Option (Paper XII). If you are a graduate, it can also be studied as part of a tailor-made course for the M.St in European Literature. You could also write your D.Phil on German film.
Whatever your interests, the best introduction to the study of film is:
David Bordwell and Kristin Thompson, Film Art: An introduction 6th edition (2001) or 7th ed. (2004).
This will give you a good understanding of technical vocabulary, issues in film studies and an overview of the history of film in 20th century.
David Bordwell, On the History of Film Style (Harvard UP, 1997)
is also a very clear and interesting survey of approaches to the history of film, with lots of information about what to look for in a shot or sequence.
One text in particular has shaped German film studies:
Siegfried Kracauer, From Caligari to Hitler: A Psychological History of the German Film (Princeton UP, 1947).
It was re-issued with a useful introduction and corrections in paperback 2004.
The bfi publish an excellent collection of essays on German film which has an up-to-date and informative bibliography on all aspects of German film:
Bergfelder, Tim, et al. (eds). The German Cinema Book (London: BFI Publishing, 2002).
There is also a very good survey of German film history:
Sabine Hake, German National Cinema (London: Routledge, 2002).
There are a number of informative web-sites, especially those of the Deutsches Institut für Filmkunde in Frankfurt and the Friedrich Wilhelm Murnau Stiftung in Wiesbaden.
The Taylor Faculty Library has a good range of films on VHS and dvd which you can take out of the library. There are also films and video/dvd players at the Language Centre.
You could start watching films
Murnau, Lang, Riefenstahl, Harlan, Herzog, Fassbinder, Treut, Tykwer
Marlene Dietrich, Hans Albers, Heinz Rühmann, Zarah Leander, Kristina Söderbaum, Marika Rökk, Klaus Kinski, Hannah Schygulla, Bruno Ganz
1920s, 1930s etc. Do not assume that 1918, 1933, 1945, 1962, 1989 is a watershed. Watch films on either side of the historical divide
Ben Morgan, Worcester College