Nationals of an EU country do not require a visa in order to enter Germany to live and work.
Non-EU citizens of "associated" countries:
Citizens of certain non-EU countries do not need a visa for entering Germany. These countries include e.g. Australia, Canada, Israel, Japan, South Korea, New Zealand and the USA. In order to find out whether you need a visa to enter Germany or not, please refer to the following list provided by the German Federal Foreign Office: https://www.auswaertiges-amt.de/en/einreiseundaufenthalt/visabestimmungen-node/staatenlistevisumpflicht-node
Non-EU citizens of all other countries:
To enter Germany you require a visa. Please contact your nearest embassy or consulate with your letter of invitation/working agreement and apply for a visa three months in advance of your arrival.