There are several ways in which you can find rental housing in Germany. The first thing to note is that furnished apartments and houses are few and far between. These rentals are favored by German locals and are much more expensive than unfurnished options.
A great way to find your housing is through online exchanges like
ImmobilienScout24. There are also provision-free (no agency fees) websites which allow you to browse for free, but do require you to pay for the contact information of landlords who currently have rentals available. NullProvision.de is a great resource for rentals that don't require an agency fee, and Studenten-WG is really good for small apartments or flat shares, and is often utilized by students searching for affordable housing. There are many local magazines and newspapers in German cities and towns which have listings. It pays to get the most recent additions as soon as they appear on newsstands, as apartments in Germany don't stay empty for very long. Toytown Munich online has a great accommodation classified section divided according to region and city. This is one of the best English language resources available. If you are using German language classifieds online or in print, it pays to familiarize yourself with common abbreviations used in these ads.