I have nearly the same understanding as whipwhitaker:
- Either you get a test 48h before entry. Negative PCR means you can bypass the quarantine. You must send the test and a form to the local Gesundheitsamt
- Or you arrive in Germany and must straight head to quarantine. You can break quarantine if you have a negative test performed 48h after entry. The test must be performed without breaking quarantine (meaning you can drive yourself to the test center but getting there on foot or via public transport is a no go). You must send the form and test result if applicable to the Gesundheitsamt
Either way I understand you must contact the Gesundheitsamt.