I think you are mixing up two concepts: One is the generic European data protection act(s) and another is the GDPR, which is German specific implementation.
The EU is quite awesome in that regard: You send complaints to your countries data protection agency.
Article 77 is just making this explicit: You complain where you are living (even cross country!), where you work or where the suspected violation took place. It doesn't say anything more.
Because of this there is no standard form to fill out: it depends on the agency itself where you choose to enter your complaint.
That's the huge downside in the German system then: in the worst case they enter a game of responsibility ping pong.