Leipzig has an excellent cultural scene and nightlife, which is best discovered by yourself! Some of the liveliest parts of town, full of bars and cafés are Barfußgäßchen and Gottschedstraße (both just to the west of the Marktplatz). The centre of student nightlife is of course the MB.
Look out for what's on magazines, usually available freely from within the bars (often in a rack in the area near the toilets, or try this), as well as postcards publicising special events. A particular highlight, well worth a visit, are the monthly nights at the unique BimboTown nightclub.
WILMA liebt euch, and to prove it they organise the weekly Monday Pub Night for international students (often attended by 100 or more students) as well as excursions most weekends during the semester time. (WILMA stands for "WillkommensInitiative für in Leipzig Mitstudierende Ausländer/innen")
Connect: —>Deutsch, organised by the SMD and LEC, is a chance for international students who do not speak any German to pick up some basics, and also meet some German students in a small, friendly environment.