The department is ranked 1st (joint with TH Karlsruhe) out of the 84 CS departments in Germany according to the ranking of the DFG (German Science Foundation), which ranks based on the amount of funding received from the DFG, cf Table A-10, column INF on p. 166 in here (see here for more info on that ranking).
TU Dortmund has several associated research institutes including the Fraunhofer Institute for Software and Systems Technology (ISST). At the TUD campus there is also the TechnologieZentrumDortmund which is apparently one of the five largest areas for technology startups in Europe, together with those in Stockholm, Berlin, Cambridge, and Sophia Antipolis.
Funding is becoming available on a recurrent basis, please check my web-site for current funding opportunities I am involved with. I am also happy to assist in applying for funding from external sources.
Information regarding organizational questions about how to pursue a PhD at TU Dortmund can be found here (in German). A short inofficial English summary is here. To sign up for PhD studies, these documents are needed.
The Office of International Relations is in charge of questions regarding international students and should be able to answer questions about being an international (PhD) student registered at TU Dortmund.