The most common website for flat offers and requests; also available in English, highly recommended:

http://www.wg-gesucht.de

 

Made by student government (AStA) of TU Dortmund and FH Dortmund; only in German and with a significantly lower number of flat offers:

http://jobsundwohnungen.asta-dortmund.de

https://www.studierbar.de/?page_id=208

 

There are also some facebook groups like...

WG & Wohnung Dortmund

TU Dortmund WG Börse

 

Also possible, but not recommended for short-term stay:

http://kleinanzeigen.ebay.de/anzeigen/s-wohnung-mieten/dortmund

http://immo.ruhrnachrichten.de/mieten/dortmund

http://www.immobilienscout24.de (watch out, they often charge you extra commission!)