Contact restrictions apply in some federal states and regions, i.e. you can only meet with a few people. The specific regulations differ from state to state. You can learn about the current regulations in your federal state in many languages at corona-was-darf-ich.de.
A distance of at least 1.50 meters should be maintained from people who do not live in the same household.
When shopping and on the bus & train, you must cover your mouth and nose with a face mask or scarf. If you do not wear a mask, you will have to pay a fine of at least 50 euros. Saxony-Anhalt is an exception: there is no fine there.
Please Note: Police officers are present to make sure everyone respects these measures and those who do not will face penalties, i.e. a fine or even prison sentence.