thank you for sharing your question with the Wefugees Community!
Unfortunately I am also not an expert on this field, but here is what I know:
First of all, are you holding any document right now? For example a Duldung? You should definetly apply for a "Aufenthaltskarte" according to FreizügG since you have the right to get one. There just might be a problem with you not having a visa, since you are in general as a foreign spouse to a EU-citizen by German Law obliged to enter with a visa. So it could happen that the Ausländerbehörde might ask you to enter again with a visa. But due to jurisdiction of the European Court of Justice they are actually not allowed to do so. Also there are some exceptions where you wouldn´t need to leave Germany and enter again.
So I would probably recommend you to try it at your local Ausländerbehörde. If they ask you for a proper visa or want you to re-enter Germany, you go see a lawyer so that he/she can help you to avoid it.
Regarding the documents: I cant tell you exactly what kind of documents they will ask from you, but I can tell you for sure that you will need: proof of your marriage such as marriage certificate, proof that your husband is working in Germany, f.e. his contract. I found this list of documents on the website of the immigration office in Berlin. If you are not from Berlin, the documents might still be the same or at least very similar:
I hope this helps. Please don´t hesitate getting back to the Wefugees Community if you have furter questions!
All the best
Note: Please keep in mind that we can´t provide qualified legal advice via the internet and that any information given can´t replace such legal advice.