Switzerland is a multilingual country by constitution. There are four national languages spoken in the different language regions: German is predominant in the north-east, in the center and in the Oberwallis. French is spoken in the west in an area called "Romandie". Italian is predominant in the Ticino and in some parts of the south of Grisons. The Romansh-speaking community in the south-east (Grisons) is the smallest. Some cantons are multilingual, i.e. language borders go beyond cantonal boundaries. Being able to communicate in more than one language has a high prestige and is strongly fostered by school curricula.
In the German-speaking region, where Zurich lies, the spoken language differs considerably from the written form. This is due to the fact that Standard German is used for written and more formal communication (for instance in the classroom), while in most other contexts Swiss dialects of German are spoken (so-called Swiss German). However, when communicating with foreigners, it's customary for most to switch to Standard German. Don't hesitate to ask people if they could talk to you in Standard German or, if necessary, in English. Especially in the university context, this is commonly accepted if not the normal case anyway.
While it may be perfectly possible to communicate in English in academia and never use a word of German, it's no secret that speaking German not only facilitates life in Zurich, it is also the key to social integration outside university. It's thus recommended to learn German. The Language Center of the University of Zurich and ETH Zurich offers a range of courses in German as a foreign language. There are classes for beginners, for advanced learners, Swiss German classes and many more. There is also a Self-Access Center for learning languages autonomously. The Language Center also organizes tandems, where two people with different mother tongues are matched in order to practice and improve their respective language skills.