A stay abroad should be well prepared in order to avoid unpleasant surprises. One of the most important aspects is to pay special attention to respecting formal preconditions for entry to and for stay at the respective host country. For entry to and stay at Germany, your country of origin is crucial:
You are not required a visa nor a residence permit for Germany. Nontheless, you have to register within 14 days after arrival in Germany at the Citizenz' Registration Office of the respective residence city in Germany. In Chemnitz, the responsible institution is the Bürgeramt (Meldebehörde). A certificate of registration counts i.a. among the preconditions to open a bank account at a German bank.
If you are coming from a non-EU country, the visa is a very important document which has to be presented already when you are entering Germany. The appropriate visa is in turn the prerequirement for the issue of a residence permit for Germany. Some countries of origin are exempted from the visa obligation but for the stay in Germany nontheless the application for a residence permit is necessary. In order to get to know, to which category your country of origin belongs, please refer to the list of countries of the Federal Foreign Office.
The information provided by the links within this category should give you first hints regarding the legal basis and the necessary documents for the entry to and stay at Germany. In the case that you are coming from a non-EU country ("third-party country") please be aware of the fact that the informated provided does not substitute to get in touch early with the responsible Immigration Authority which is the central contact point for foreigners from "third-party countries" in all issues regarding right of residence.