To marry in Germany, she should contact her local marriage registry office (in German ‘Standesamt’). She can make an appointment to get married once she has submitted the documents the Standesamt require from both of you. As a rule these are:
- Birth certificate
- Certificate of eligibility to marry (in German ‘Ehefähigskeitszeugnis’, whether you need this depends on your nationalities)
She should be aware that any documents and information she provides to the Standesamt can be shared with the immigration authorities. If you require a visa for Germany, then you have to decide whether to opt for a Schengen visa or a specific visa for getting married. You may have difficulties here due to her residency status if she is the one inviting you; at the very least she will have to show that she can financially cover your costs here.
Once married, she can start the process of applying for a United States visa as your spouse but here I do not know what the conditions are. For that information you can **** at the website of the U.S. embassy in Germany.