Europe makes it possible! Since the EU's laws on freedom of movement apply to you as a European citizen, you typically need neither an entry visa nor a residence permit to stay in Germany. You can also travel and work as you like in the country. However, you do need a valid passport or another form of personal identification, and you are required – just as all German citizens are – to register with the local registry office (Meldebehörde). This office will collect all of the information pertaining to the applicable freedom of movement regulations and transfer it to the foreign citizens' office (Ausländerbehörde). If you eventually require documentation regarding your right to move freely within the EU, the foreign citizens' office will issue you a corresponding certificate free of charge. Immediate family members of EU citizens receive EU residence permits.
If you are a citizen of Switzerland and stay in Germany for longer than three months, you are also required to register with the foreign citizens' office. Its officials will then verify whether you meet the requirements of EU's freedom of movement laws based on the related agreement between the EU and Switzerland. If you do, you will receive a residence permit (for a fee).