Unfortunately, most German universities do not offer accommodation to enrolling students. This means that finding accommodation is up to you. With little to no tuition fees in Germany, rent is likely to be your biggest monthly expense, and this will vary depending on which part of the country you live in. In big cities within Western Germany (i.e. Dusseldorf, Cologne etc.) and smaller, student-oriented cities such as Heidelberg and Freiburg, you should expect to pay slightly more than if you were living in eastern Germany (i.e. Berlin).
When looking for accommodation in Germany, you should consider student residences, shared accommodation or an apartment. An unshared apartment is the most expensive choice, and this will generally cost in the region of €350-400 (~US$300-340) a month. Shared accommodation would be cheaper at around €250-300 (~US$210-250) a month, while student residences are cheaper yet again at around €200-250 (~US$170-210) a month.
If you struggle with finding accommodation, you can also look for somewhere temporary to cover your first few days or weeks in the country. In these instances, emergency housing may be provided by the university or you could try couch-surfing, staying in a hostel, B&B or hotel.
For more information on finding accommodation visit this article on the DAAD website. You could also use the Study-in-de’s accommodation finder, which includes information, addresses and application details on a large selection of student residence halls in Germany.