If you want to start a doctorate in Germany, there are various ways to do so: You can apply for open positions at university chairs or in a doctoral programme. But you can also contact a possible supervisor directly. You can find an overview of the different ways here.
Young researchers of Jena University who are planning a research stay abroad during their doctorate, may apply to funding schemes that support these research stays. It is also possible to combine a research stay abroad with the participation in an international conference and a workshop.