Degrees that were awarded as PhD are styled as such in Germany and written after the name. Doctoral degrees that are awarded in Germany or the EU can permit you to shorten from "Dr. rer. nat." to just "Dr." before your name. Using a doctorate that you have not been awarded is a serious crime in Germany and can bring stiff fines and even a year's jail time. See StgB § 132a.
Doctorates awarded outside of the EU have to be formally recognized by the state education ministry and then the name of the granting university has to be appended. For example, our Russian instructor uses:
Dr. (Staatliche Kuban-Universität)
If you have defended your doctorate but haven't published your thesis yet (mandatory for using the doctoral degree in your name) you are permitted to write "Dr. des." (designated). You also don't have to correct people who mislabel you "Dr." anymore.
If you went to the Czech Republic or Slovakia and got one of their PhDr degrees thinking it was a doctorate, you lose. For bizarre reasons, it is only recognized in Bavaria and Berlin as being worthy of the "Dr.", not in the rest of the states. The former Minister of Transportation was thus "Dr." when leaving home in Munich, not "Dr." during the flight to Berlin, and "Dr." again when he landed.
If you have two doctorates, then Dr. Dr. is used. If you have a professorship (and only then, not when you are just an instructor) then you may use Prof. Dr.
At Universities of Applied Sciences you may still encounter the style "Prof. Dipl.-Inform.", which is what I was until I got my doctoral dissertation published.
When speaking German, you research and use the proper titles. People on the same level (i.e. professor to professor, doctor to doctor) do not use any titles. Speaking English will vary by field. In Computer Science we generally try to avoid using titles, if we have to and are speaking "up" we would use just "Dr." or "Prof.". If you read German, there is a nice long article, and of course many more at sites that sell phony doctorates.
Some relevant comics for English: PHD Comics - What should I call my professor?