Tests for the coronavirus are available to travelers at German airports. This includes an RT-PCR test (Reserve Transcription Polymerase Chain Reaction test) which determines whether an acute COVID-19 infection is present.
New regulations for travelers entering Germany from a high-risk area

In North Rhine-Westphalia, testing will be mandatory for all travelers returning from risk areas as of 28 December 2020. The test must not be older than 24 hours at the time of entry or must be carried out 24 hours after entry at the latest. Antigen tests and PCR tests are permitted. The costs for the test must be covered by the passenger.

In Bavaria, testing is already mandatory for travelers returning from risk areas. The test may not be older than 48 hours at the time of entry or must be carried out 72 hours after entry at the latest. For travelers returning from risk areas, there is an additional quarantine obligation for 10 days, which can be terminated at the earliest after the fifth day and following a negative test result regarding infection with the SARS-CoV-2 coronavirus. Separate quarantine regulations apply to travelers from the United Kingdom and Northern Ireland as well as South Africa.

Since 8 November 2020, travelers arriving in Germany from countries considered to be coronavirus high-risk areas have been required to self-isolate for 10 days. They have the option of paying for a COVID-19 test after five days and ending their self-isolation early if the test is negative.

Germany’s new model quarantine regulation stipulates that certain groups of people may be exempted from the obligation to self-isolate by a negative test result under certain conditions (e.g. demonstrably necessary business trips of up to five days). Since 1 December 2020 travelers arriving from high-risk areas have been required to pay for their coronavirus tests. Test centres are available at Frankfurt, Munich and many other German airports if you need a coronavirus test.
Regulations for persons entering Germany in connection with coronavirus SARS-CoV-2/COVID-19 (PDF)

To find out which regions are currently considered to be official high-risk areas and entry from which requires a 10-day self-isolation period, please consult the websites of the German Government and the Robert Koch Institute.
To official information from the Robert Koch Institute

To the German Government’s travel warnings