Whether or not you need a visa and a residence permit for entry to Germany depends on your nationality and on the purpose of your stay. Citizens of the United States of America, Australia, Canada, Israel, Japan, New Zealand, Switzerland, as well as EU citizens may apply for their residence permit after entering Germany without a visa.

All other nationals are required are required to apply and obtain a residence permit prior to entry (an option also open to US citizens). US citizens may inquire and apply at the German Embassy in Washington, the Consulates in Atlanta, Boston, Chicago, Houston, Los Angeles, Miami, New York or San Francisco. Detailed information may be obtained from:

http://www.germany.info/relaunch/info/consular_services/visa/study.html