How do I become a resident of Germany?

You are technically already a resident of Germany if you have any long-stay visa or temporary/current residence permit. But, if you want to become a permanent resident of Germany, then you need to apply for a permanent residence permit.
These are only issued after living in Germany for a period of more than five years, and you must have had a temporary residence permit or visa for that length of time. You will need to have sufficient knowledge of the German language, as well as an understanding of local legal and social order and German society as a whole.