First of all you have to register your wedding at the Registry Office (“Standesamt”).
The proper authority to consult is the Registry Office of the district of the applicant’s primary, secondary or habitual residence. If the couple have different residences they can choose between the different offices.
In Germany you can get married if you are of age, i.e. 18 years old or more, have unlimited legal competence (usually the case) and unmarried. Existing registered same-sex partnerships can be changed to become a marriage.
Please inquire at the Registry Office to learn which documents will be needed in your concrete case.
It is desirable for both partners of the future marriage to be present during the application interview.